Janus Cosmological Model

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File:RSC 0023.9.jpg

The Janus cosmological model is an alternative theoretical cosmological model developed by controversial French physicist Jean-Pierre Petit (and collaborators) based on an idea by Andrei Sakharov. It has been described as a "theory that is indeed minority and dissident compared to the theories most in vogue among astrophysicists" by Cédric Villani.

The model describes a structure of the universe composed of two sectors interacting through gravitation, one containing matter with positive mass (our observable universe) and the other containing matter with negative mass (not directly observable).

This theory was developed to resolve several observational anomalies and unresolved theoretical problems in the standard cosmological model (ΛCDM), notably:

• matter-antimatter asymmetry in the universe
• the unexplained origin of dark energy and dark matter
• the cosmological horizon problem
• the nature of singularities in black holes
• the large-scale structure of the universe as a "soap bubble"

Theoretical foundations

The Janus model is based on the physics of dynamical groups and symplectic geometry developed by Jean-Marie Souriau. These principles include:

Interpretation of T-symmetry (time reversal)

According to Souriau's work, the inversion of the temporal coordinate (T-symmetry) leads to an inversion of energy. In the Poincaré group, the time reversal operator applied to the motion of a particle transforms its energy from E to −E, which leads to the inversion of its mass. This allows a physical interpretation of Sakharov's idea: his second universe would be composed of particles having both negative energy and negative mass.

CPT symmetry and negative masses

The model extends the concept of CPT symmetry (Charge, Parity, Time) by introducing the possibility of negative masses as a CPT symmetric counterpart to positive masses. While C-symmetry (charge conjugation) transforms matter into antimatter while preserving positive mass, the combined PT symmetry (parity and time reversal) reverses the sign of mass.

Geometric interpretation of electric charge

Based on the Kaluza-Klein model, the Janus model interprets electric charge as a geometric component resulting from a compactified fifth dimension. According to Noether's theorem, this additional symmetry is associated with the conservation of electric charge.

Janus dynamical group

The model defines a "Janus group" that combines C-symmetry (matter-antimatter) and PT-symmetry (space-time inversion) in a single theoretical framework:

$g:=\{\left(\begin{array}{ccc}\lambda \mu & 0& \varphi \\ 0& \lambda L_o& C\\ 0& 0& 1\end{array}\right),\lambda ,\mu \in \{-1,1\}\cap \varphi \in \mathbb{ℝ}\cap L_o\in Lo{r}_o\cap C\in {\mathbb{ℝ}}^{1,3}\}$

This group allows for describing the interactions between matter, antimatter, and negative mass particles in a consistent relativistic context.

Mathematical structure

The Janus model is an extension of general relativity described by a bimetric structure in which spacetime is simultaneously endowed with two distinct metrics that interact with each other.

Bimetric model

Spacetime is considered as a four-dimensional manifold with two metrics: $g_{\mu \nu }$ to describe the motion of positive mass matter and ${\overline{g}}_{\mu \nu }$ to describe the motion of negative mass matter. The two metrics share the same coordinates $(x^0,x^1,x^2,x^3)$ but they generate different geodesics that determine the motion of the two matter populations.

Coupled field equations

The action of the model is formulated as follows:

$A=\underset{E}{\int }[\frac{1}{2\chi }R+S_{+}+S_{-}]\sqrt{|g|}{d}^{4}x+\underset{E}{\int }[\frac{\kappa }{2\overline{\chi }}\overline{R}+{\overline{S}}_{+}+{\overline{S}}_{-}]\sqrt{|\overline{g}|}{d}^{4}x$

Applying the principle of least action with $\kappa =-1$, we obtain the two coupled field equations:

$R_{\mu \nu }-\frac{1}{2}{g}_{\mu \nu }R=\chi (T_{\mu \nu }+\sqrt{\frac{|\overline{g}|}{|g|}}{\overline{T}}_{\mu \nu })$

${\overline{R}}_{\mu \nu }-\frac{1}{2}{\overline{g}}_{\mu \nu }\overline{R}=-\overline{\chi }({\overline{T}}_{\mu \nu }+\sqrt{\frac{|g|}{|\overline{g}|}}{T}_{\mu \nu })$

Where $T_{\mu \nu }$ and ${\overline{T}}_{\mu \nu }$ are the energy-momentum tensors of the two populations, while the cross terms describe how each population influences the geometry of the other.

Generalized energy conservation

For homogeneous and isotropic FLRW cosmological solutions, the Janus model imposes a compatibility relation that corresponds to a generalized energy conservation:

$\rho c^2{a}^3+\overline{\rho }{\overline{c}}^2{\overline{a}}^3=E=\text{constant}$

Where $\rho$ and $\overline{\rho }$ are the energy densities of the two populations, $a$ and $\overline{a}$ are their respective scale factors. This relation suggests that the observed acceleration of the expansion of the universe would be due to a negative total energy $E$.

Topology of the model

The topological structure of the Janus model fundamentally distinguishes it from the standard cosmological model as it posits a closed geometry of the universe, without singularities.

Double-skin structure

The model proposes that the universe has the topology of a four-dimensional sphere $S^4$ that forms a double covering of the projective space $P^4$. In this structure:

• Antipodal points, representing the Big Bang and Big Crunch, coincide
• The two "faces" of the universe are PT-symmetric
• The structure naturally allows for the emergence of P and T symmetries

Elimination of singularities

An important consequence of the model is the replacement of singularities by a tubular structure:

• Singularities are eliminated through a connection between the two sectors
• The resulting structure is topologically equivalent to the double shell of a Klein bottle
• This configuration allows for a transition between the two sectors of the universe

Mathematical formalism

The topological structure can be described locally by the neighborhood of a meridian line, configured as the double covering of a Möbius strip with three half-twists. This structure is analogous to the Boy surface, which represents the immersion of the projective plane $P^2$ in ${\mathbb{ℝ}}^3$.

Physical consequences

This topological structure has important implications:

• Provides a geometric basis for mass inversion
• Naturally explains the existence of the two sectors of the universe
• Eliminates the problem of initial and final singularities
• Allows for a smooth transition between positive and negative masses

Predictions and observations

The Janus cosmological model provides explanations and predictions for several astronomical and cosmological phenomena, some of which have been confirmed by recent observations.

Large-scale structure of the universe

One of the main predictions of the Janus model concerns the distribution of matter at large scales:

• Formation of a lacunary structure with large cosmic voids
• Negative mass conglomerates at the center of these voids
• Filaments and "walls" of galaxies at the interfaces between these voids
• Galaxy clusters at the nodes of this structure

This prediction has been confirmed by large-scale mapping of the universe carried out by Hoffman, Pomarède, Tully, and Courtois in 2017, which revealed the presence of large cosmic voids, such as the "dipole repeller".

Acceleration of cosmic expansion

The Janus model offers an alternative explanation to dark energy for the accelerated expansion of the universe:

• The acceleration is caused by gravitational repulsion between positive and negative masses
• The total energy of the universe is negative, as expressed by the generalized conservation relation
• This interpretation has been successfully compared with observations of Type Ia supernovae

Early formation of stars and galaxies

The model predicts accelerated formation of the first stars and galaxies:

• Negative mass conglomerates confine positive matter in slab-like structures
• This compression accelerates radiative cooling and gravitational instability
• This process enables the formation of fully developed galaxies within the first few hundred million years after the Big Bang

This prediction has been confirmed by recent observations from the James Webb Space Telescope, which revealed mature and structured galaxies at very high redshifts (z>7).

Negative gravitational lensing effect

A unique prediction of the Janus model is the "negative gravitational lensing" effect:

• Negative mass conglomerates act as diverging lenses
• This effect decreases the apparent brightness of background galaxies
• The effect should be particularly visible around large cosmic voids, such as the dipole repeller
• The distribution of this effect should follow a "ring" pattern

This prediction could be verified through dedicated observations of regions surrounding identified large cosmic voids.

Comparison with the ΛCDM model

The Janus model is proposed as an alternative to the standard ΛCDM cosmological model, offering different explanations for phenomena that, in the standard model, require the introduction of ad hoc epicycles.

Alternative to dark entities

In the standard cosmological model, approximately 95% of the universe's content consists of hypothetical components:

• 27% dark matter (attractive, non-baryonic)
• 68% dark energy (repulsive, with equation of state $w=-1$)
• 5% ordinary baryonic matter

The Janus model instead proposes:

• 95% negative mass (invisible because it emits negative energy photons)
• 5% ordinary positive mass matter
• No need for dark matter or dark energy

Matter-antimatter asymmetry

• ΛCDM model: does not offer a satisfactory explanation for the absence of primordial antimatter in the universe
• Janus model: proposes, following Sakharov, that negative mass antimatter exists in the other sector of the universe, restoring a global symmetry

Resolved problems

The Janus model would resolve several problems of the standard model:

• Horizon problem: naturally resolved by the topological structure of the universe
• Black hole singularities: eliminated by the mass inversion process
• Dipole repeller problem: explained by negative mass concentrations
• Early galaxy formation: explained by the confinement of positive matter between negative mass conglomerates

Criticisms and responses

The Janus model has been criticized and its mathematical and physical consistency questioned.

Criticisms by Thibault Damour

In 2022, theoretical physicist Thibault Damour published a critical analysis of the Janus model, raising several decisive objections:

• Absence of general covariance due to the introduction of a "constant diagonal matrix"
• Inconsistencies in the Tolman-Oppenheimer-Volkoff equations derived from the model
• Contradictions with the action-reaction principle

Responses and model development

In response to these criticisms, Petit and his collaborators published several articles to improve certain aspects of their formalism:

• Proof of mathematical consistency in the weak field limit (Newtonian approximation)
• Verification of general energy conservation
• Satisfaction of Bianchi identities

After asking Cédric Villani to take a position in this controversy, Villani stated that Petit had not responded to Damour's objections, which provoked Petit's anger, who threatened to "destroy Villani's reputation".

Defenders of the Janus model argue that these technical difficulties do not call into question the model's observational predictions and that the history of science shows that mathematically imperfect theories can nevertheless point toward fruitful physical ideas.

Publications and recent developments

The Janus model has been progressively developed in numerous scientific publications that progressively integrate new observations and criticisms.

Chronological development of the model

• 1977–1995: First publications on the concepts of twin universes and negative masses
• 1994–2000: Development of the bimetric model and first numerical simulations
• 2014–2015: Complete mathematical formalization of the model
• 2018–2019: Comparison with observational data and responses to criticisms
• 2024: Publication of the most complete and updated version in the European Physical Journal C

Comparison with James Webb Telescope observations

Recent observations from the James Webb Space Telescope have provided new data that could support some predictions of the Janus model:

• Identification of fully formed galaxies at redshift z>7 (less than 700 million years after the Big Bang)
• Galaxies with already old stars and barred spiral structures at high redshifts
• Stellar masses between 10¹⁰ and 10¹¹ solar masses, difficult to explain in the context of the ΛCDM model..

Future perspectives

The Janus model suggests testable possibilities through future observations:

• Detailed mapping of negative gravitational lensing around large cosmic voids
• Statistical analysis of the distribution and brightness of high-redshift galaxies
• New measurements of the Hubble constant and comparison with model predictions
• Studies on the structure and age of primordial galaxies

References

Category:Theoretical physics Category:Relativity Category:Cosmology Category:Alternative cosmologies Category:Fringe physics

File:RSC 0023.9.jpg

The Janus cosmological model is an alternative theoretical cosmological model developed by controversial French physicist Jean-Pierre Petit (and collaborators) based on an idea by Andrei Sakharov. It is described as a "theory that is indeed minority and dissident compared to the theories most in vogue among astrophysicists" by Cédric Villani. The model describes a structure of the universe composed of two sectors interacting through gravitation, one containing matter with positive mass (our observable universe) and the other containing matter with negative mass (not directly observable). This theory was developed to address several observational anomalies and unsolved theoretical problems in the standard cosmological model (ΛCDM), notably:

the matter-antimatter asymmetry in the universe the unexplained origin of dark energy and dark matter the cosmological horizon problem the nature of singularities in black holes the "soap bubble" large-scale structure of the universe

Theoretical foundations

The Janus model is based on the physics of dynamical groups and symplectic geometry developed by Jean-Marie Souriau. These principles include:

Interpretation of T-symmetry (time reversal)

According to Souriau's work, the inversion of the time coordinate (T-symmetry) leads to an inversion of energy. In the Poincaré group, the time reversal operator applied to the motion of a particle transforms its energy from E to -E, which leads to the inversion of its mass. This provides a physical interpretation of Sakharov's idea: his second universe would be composed of particles having both negative energy and negative mass.

CPT symmetry and negative masses

The model extends the concept of CPT symmetry (Charge, Parity, Time) by introducing the possibility of negative masses as the CPT-symmetric counterpart of positive masses. While C-symmetry (charge conjugation) transforms matter into antimatter while preserving positive mass, combined PT symmetry (parity and time reversal) reverses the sign of mass.

Geometric interpretation of electric charge

Based on the Kaluza-Klein model, the Janus model interprets electric charge as a geometric component resulting from a compactified fifth dimension. According to Noether's theorem, this additional symmetry is associated with the conservation of electric charge.

Janus dynamical group

The model defines a "Janus group" that combines C-symmetry (matter-antimatter) and PT symmetry (spacetime inversion) within a single theoretical framework: Failed to parse (syntax error): {\displaystyle g := \left{ \begin{pmatrix} \lambda\mu & 0 & \phi \ 0 & \lambda L_o & C \ 0 & 0 & 1 \end{pmatrix}, \lambda,\mu \in {-1, 1} \cap \phi \in \mathbb{R} \cap L_o \in Lor_o \cap C \in \mathbb{R}^{1,3} \right} } This group enables the description of interactions between matter, antimatter, and negative mass particles within a consistent relativistic framework.

Mathematical structure

The Janus model is an extension of general relativity described by a bimetric structure in which spacetime is simultaneously endowed with two distinct metrics that interact with each other.

Bimetric model

Spacetime is considered as a four-dimensional manifold with two metrics: $g_{\mu \nu }$ to describe the motion of positive mass matter and ${\overline{g}}_{\mu \nu }$ to describe the motion of negative mass matter. The two metrics share the same coordinates $(x^0,x^1,x^2,x^3)$ but they generate different geodesics which determine the motion of the two matter populations.

Coupled field equations

The action of the model is formulated as follows: $A=\underset{E}{\int }[\frac{1}{2\chi }R+S_{+}+S_{-}]\sqrt{|g|},d^{4}x+\underset{E}{\int }[\frac{\kappa }{2\overline{\chi }}\overline{R}+\overline{S}++\overline{S}-]\sqrt{|\overline{g}|},d^{4}x$ By applying the principle of least action with $\kappa =-1$, we obtain the two coupled field equations: $R_{\mu \nu }-\frac{1}{2}{g}_{\mu \nu }R=\chi (T_{\mu \nu }+\sqrt{\frac{|\overline{g}|}{|g|}}{\overline{T}}_{\mu \nu })$ $\overline{R}\mu \nu -\frac{1}{2}\overline{g}\mu \nu \overline{R}=-\overline{\chi }(\overline{T}\mu \nu +\sqrt{\frac{|g|}{|\overline{g}|}}T\mu \nu )$ Where $T_{\mu \nu }$ and ${\overline{T}}_{\mu \nu }$ are the energy-momentum tensors of the two populations. The interaction terms describe how each population influences the geometry of the other.

Generalized energy conservation

For homogeneous and isotropic FLRW cosmological solutions, the Janus model imposes a compatibility relation which corresponds to a generalized energy conservation: $\rho c^2{a}^3+\overline{\rho }{\overline{c}}^2{\overline{a}}^3=E=\text{constant}$ Where $\rho$ and $\overline{\rho }$ are the energy densities of the two populations, $a$ and $\overline{a}$ are their respective scale factors. This relation suggests that the observed acceleration of the universe's expansion would be due to a negative total energy $E$

Topology of the model

The topological structure of the Janus model fundamentally distinguishes it from the standard cosmological model as it posits a closed geometry of the universe, without singularities.

Double-skin structure

The model proposes that the universe has the topology of a four-dimensional sphere $S^4$ which forms a double cover of the projective space $P^4$. In this structure:

The antipodal points, representing the Big Bang and the Big Crunch, coincide The two "faces" of the universe are PT-symmetric The structure naturally allows the emergence of P and T symmetries

Singularity elimination

An important consequence of the model is the replacement of singularities with a tubular structure:

Singularities are eliminated through a connection between the two sectors The resulting structure is topologically equivalent to the double cover of a Klein bottle This configuration allows a transition between the two sectors of the universe

Mathematical formalism

The topological structure can be locally described by the neighborhood of a meridian line, configured as the double cover of a Möbius strip with three half-twists. This structure is analogous to Boy's surface, which represents the immersion of the projective plane $P^2$ in ${\mathbb{ℝ}}^3$

Physical consequences

This topological structure has important implications:

It provides a geometric basis for mass inversion It naturally explains the existence of the two sectors of the universe It eliminates the problem of initial and final singularities It allows a smooth transition between positive and negative masses

Predictions and observations

The Janus cosmological model provides explanations and predictions for several astronomical and cosmological phenomena, some of which have been confirmed by recent observations.

Large-scale structure of the universe

One of the main predictions of the Janus model concerns the distribution of matter on large scales:

Formation of a lacunar structure with large cosmic voids Concentrations of negative mass at the center of these voids Filaments and "walls" of galaxies at the interfaces between these voids Galaxy clusters at the nodes of this structure

This prediction was confirmed by the large-scale mapping of the universe carried out by Hoffman, Pomarède, Tully and Courtois in 2017, which revealed the presence of large cosmic voids, such as the "dipole repeller".

Acceleration of cosmic expansion

The Janus model offers an alternative explanation to dark energy for the accelerated expansion of the universe:

The acceleration is caused by gravitational repulsion between positive and negative masses The total energy of the universe is negative, as expressed by the generalized conservation relation

This interpretation has been successfully compared to Type Ia supernova observations.

Early formation of stars and galaxies

The model predicts accelerated formation of the first stars and galaxies:

Negative mass concentrations confine positive matter in sheet-like structures This compression accelerates radiative cooling and gravitational instability This process enables the formation of fully developed galaxies within the first hundreds of millions of years after the Big Bang

This prediction was confirmed by recent observations from the James Webb Space Telescope, which revealed mature and structured galaxies at very high redshifts (z>7):..

Negative gravitational lensing effect

A unique prediction of the Janus model is the "negative gravitational lensing" effect:

Negative mass concentrations act as diverging lenses This effect decreases the apparent brightness of background galaxies The effect should be particularly visible around large cosmic voids, such as the dipole repeller The distribution of this effect should follow a "ring" pattern

This prediction could be verified through dedicated observations of regions surrounding identified large cosmic voids.

Comparison with the ΛCDM model

The Janus model is proposed as an alternative to the standard ΛCDM cosmological model, offering different explanations for phenomena that, in the standard model, require the introduction of ad hoc epicycles.

Alternative to dark entities

In the standard cosmological model, approximately 95% of the universe's content consists of hypothetical components:

27% dark matter (attractive, non-baryonic) 68% dark energy (repulsive, with equation of state $w=-1$) 5% ordinary baryonic matter

The Janus model proposes instead:

95% negative mass (invisible because it emits negative-energy photons) 5% ordinary positive mass matter

No need for dark matter or dark energy

Matter-antimatter asymmetry

ΛCDM model: does not offer a satisfactory explanation for the absence of primordial antimatter in the universe. Janus model: following Sakharov, it proposes that negative-mass antimatter exists in the other sector of the universe, restoring global symmetry.

Problems resolved

The Janus model would resolve several problems of the standard model:

Horizon problem: naturally resolved by the topological structure of the universe Black hole singularities: eliminated by the mass inversion process Dipole repeller problem: explained by negative mass concentrations Early galaxy formation: explained by the confinement of positive matter between negative mass concentrations

Criticisms and responses

The Janus model has been criticized and its mathematical and physical consistency questioned.

Criticisms by Thibault Damour

In 2022, theoretical physicist Thibault Damour published a critical analysis of the Janus model, raising several decisive objections

Absence of general covariance due to the introduction of a "constant diagonal matrix" Inconsistencies in the Tolman-Oppenheimer-Volkoff equations derived from the model Contradictions with the action-reaction principle

Responses and model development

In response to these criticisms, Petit and his collaborators published several articles to improve certain aspects of their formalism:

Proof of mathematical consistency in the weak field limit (Newtonian approximation) Verification of general energy conservation Satisfaction of Bianchi identities

After asking Cédric Villani to take sides in this controversy, the latter considered that Petit had not responded to Damour's objections, which provoked Petit's anger, who threatened to "destroy the reputation" of Villani. Defenders of the Janus model maintain that these technical difficulties do not invalidate the model's observational predictions and that the history of science shows that mathematically imperfect theories can nevertheless point toward fruitful physical ideas.

Publications and recent developments

The Janus model has been progressively developed in numerous scientific publications that gradually integrate new observations and criticisms.

Chronological development of the model

1977-1995: first publications on the concepts of twin universes and negative masses 1994-2000: development of the bimetric model and first numerical simulations 2014-2015: complete mathematical formalization of the model 2018-2019: comparison with observational data and responses to criticisms 2024: publication of the most complete and up-to-date version in the journal European Physical Journal C

Comparison with James Webb Space Telescope observations

Recent observations from the James Webb Space Telescope have provided new data that could support certain predictions of the Janus model:

Identification of fully formed galaxies at redshift z>7 (less than 700 million years after the Big Bang) Galaxies with already old stars and barred spiral structures at high redshifts Stellar masses between 10¹⁰ and 10¹¹ solar masses, difficult to explain in the context of the ΛCDM model

Future perspectives

The Janus model yields testable possibilities through future observations:

Detailed mapping of negative gravitational lensing around large cosmic voids Statistical analysis of the distribution and brightness of high-redshift galaxies New measurements of the Hubble constant and comparison with model predictions Studies on the structure and age of primordial galaxies

References

Category:Pages with unreviewed translations Category:Cosmology Category:Theory of relativity Category:Theoretical physics

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