Discrete Symmetries and GR: The Dark Side of Gravity (gr-qc & ) Frédéric Henry-Couannier CPPM/RENOIR Marseille

Plan Negative energies in QFT (gr-qc ) Cosmology Gravitational waves Local gravity Pioneer effect Outlooks and conclusion  Modified GR needed

Negative Energies, Tachyons ? The Lorentz group has negative energy and tachyonic representations. Why not E<0 ?: -h  -mc 2, -(  mc 2 ~-1/2 mv 2 (v<<c) Usual answer: – Unavoidable instabilities – E<0 not observed Natural symmetries: - Time reversal - x/t symmetry: +--- => -+++

E<0 in Relativistic QFT E<0 quantum fields are solutions of relativistic equations. Maximum action principle needed.  Opposite Quantum Fields vacuum divergences.

Unitary Time reversal Unitary T But we also need  Impossible in SR  Modified GR needed ( )

Discrete Symmetries in GR Locally inertial frame transforms as:  Discrete symmetry gives nothing new in GR

Discrete Symmetries in modified GR There is a privileged coordinate system x T Symmetry keeps discrete: generates a second inertial frame hence another metric

Conjugate actions under discrete symmetries Discrete Symmetry

Scalar action Conjugate metrics are linked  Only gravity (!) will connect the conjugate worlds Discrete Symmetry

The Conjugate metrics Time reversal:  Negative energy objects live in x/t symmetry:  Tachyonic objects live in

The metrics are complex (needed for +---  -+++) We can isolate moduli and phases equations:

Modified Einstein equations is not covariant  true only in the privileged frame. New equations Extremum action & eliminate

Isotropy and space/time signature symmetry Conjugate metrics are in isotropic form Space/time signature symmetry : -+++  +---  Two possible metrics:

Action Modified GR and discrete symmetries Metrics Modulus (background) Modulus (background) Phase (perturbation) Phase (perturbation)

B=-A(moduli)  cosmology Equation:  Spatially flat universes a(t)a -1 (t) t 1 t=0

Magnitude vs redshift SNA test (SCP 2003) Fitting  in SCP 2003 Statistical error only  2 =49. (54 ndof)  = 1.6±0.3(stat)  q 0 =-0.38±0.07

Rayon de l’univers RG conventionnelle: Inverser le temps = remonter dans le temps :Inversion du temps RG modifiée: Inverser le temps = sauter dans un autre univers

Cosmology Flat Universe (no inflation) Constant acceleration ( no ) t  -t  no paradox No Big-Bang singularity Very small expanding rate near t=0  no Horizon

B=-A phase, Cosmic Waves CW propagate at c CW monopolar in privileged frame No auto-coupling but CW carry energy  Same binary pulsar decay rate as in GR Same radiated power by rotating body:

Solution: In GR: B=1/A, phase  local gravity

 Local gravity (II) As in GR up to PN order No Schwarzschild Singularity No gravitationnal wave. Instantaneous Gravity. Objects in the same metric attract each other Objects in different metrics reppel each other  Stable with E<0!

Local gravity (III): Gravitomagnetism in GPB ( ) Preferred frame effect Unic cosmological privileged frame ? - No frame dragging - Large oscillating PF effect in GP-B Many elementary privileged frames ? - As in GR Solar systems privileged frames ? - No frame dragging - Small PF effect in GP-B

 Local gravity (IV) CMB preferred directions  privileged directions effects in CMB! Equivalent to bad corrections of Doppler effects ~dz/z~10 -8 Large enough to account for the CMB quadrupôle ?

B=1/A, modulus: Pioneer Effect Régime 1: away from sources B=-A  Red-shift + cosmic waves Régime 2: in the vicinity of sources B=1/A  Blue-shift At the frontier: a metric discontinuity

No arbitrary hypothesis Anti-unitary time reversal Isotropy, x/t gravity, cosmology, CW, Pioneer Conjugate complex metrics

RG+discrete symmetries  E<0 (stable!) Universe flatness and acceleration Pioneer effect Nor Big bang neither BH singularity Caustics and lensing effects Pseudo-Horizon effect Vacuum divergences compensation

Outlooks (I): From the CMB to large scale structures Still quasi stationary cosmology near t=0 Baryonic matter only  Exponentially growing fluctuations early reach the nonlinear regime  Raw typical sizes of galaxies (our universe structures) vs universe voids (conjugate universe structures)  Raw typical visible masses of galaxies

Outlooks (II): From t=0 to the CMB Stationary gravitational waves in a finite volume are primordial fluctuations  acoustic peaks again !? No horizon  CMB large scale homogeneity Acoustic peaks only sensitive to curvature and CMB physics !? Inflation in trouble at large scale (quadrupôle and octopôle) !?

Outlooks (III): No need for dark matter ? Universe twice older: 26 billion years Oldest galaxies (z=5): 17 billion years Galaxy creates a void in conjugate universe equivalent to a Halo Caustic  repulsive shell around galaxy?

Conclusion If the model is « crazy enough to be true »: A new window opens on fascinating theoretical, phenomenological and experimental outlooks ! With the instantaneous gravity world : A new window opens on … much more …

x/t symmetry Most general form for the metrics:  If, C violates x/t symmetry 

x/t symmetry (II) If A=i:  x/t symmetry OK 

Action Modulus: Time conjugate universes Phase: Cosmic Waves SourceSolutions&interpretation Modulus: Pioneer effect Phase: Gravity Modified GR and discrete symmetries Metrics