Dark Energy & High-Energy Physics

Dark Energy & High-Energy Physics Jérôme Martin Institut d’Astrophysique de Paris

P. Brax & J. Martin, Phys. Lett. B, 40 (1999), astro-ph/9905040 • P. Brax & J. Martin, Phys. Rev. D 61, 103502 (2000), astro-ph/9912046 • P. Brax , J. Martin & A. Riazuelo, Phys. Rev. D 62, 103505 (2000), astro-ph/0005428 • P. Brax , J. Martin & A. Riazuelo, Phys. Rev. D 64, 083505 (2001), hep-ph/0104240 • J. Martin & M. Musso, Phys. Rev. D, to appear, astro-ph/0410190 Outline • Measuring the accelerated expansion • Quintessence: basics • Implementing Quintessence in high energy physics • Quintessence and its interaction with the “ rest of the world”: the • case of the inflaton field • Conclusions References: • P. Brax & J. Martin, Phys. Rev. D 71, 063530 (2005), astro-ph/0502069

Measuring the expansion with the SNIa

Consequences & Remarks This is a pure kinematical measurement (no dynamics) of the luminosity distance The Universe is accelerating The Friedmann equation with pressureless matter does not describe correctly the observations

Consequences & Remarks This is a pure kinematical measurement (no dynamics) of the luminosity distance The Universe is accelerating [J. L. Tonry et al., Astrophys. J 594, 1 (2003), astro-ph/0305008] The Friedmann equation with pressureless matter does not describe correctly the observations [W. Freedman & M. Turner, Rev. Mod. Phys. 75, 1433 (2003), astro-ph/0308418]

Consequences & Remarks This is a pure kinematical measurement (no dynamics) of the luminosity distance The Universe is accelerating The Friedmann equation with pressureless matter does not describe correctly the observations

Consequences & Remarks This is a pure kinematical measurement (no dynamics) of the luminosity distance Possibility 1: The observations are not correct, e.g. the SNIa are not standard candels (dust, evolution etc …) The Universe is accelerating The Friedmann equation with pressureless matter does not describe correctly the observations

Consequences & Remarks This is a pure kinematical measurement (no dynamics) of the luminosity distance Possibility 2: Gravity is modified The Universe is accelerating New “large” characteristic scale The Friedmann equation with pressureless matter does not describe correctly the observations

Consequences & Remarks This is a pure kinematical measurement (no dynamics) of the luminosity distance There is a missing component or the stress-energy tensor is not “correct” Possibility 3: The Universe is accelerating Possible candidates include … • Cosmological constant • Scalar field (quintessence) • Extented quintessence • K-essence • Chaplygin gas-Quartessence • Bulk viscosity • Super-horizon modes • Quantum cosmological effect • etc … The Friedmann equation with pressureless matter does not describe correctly the observations

Consequences & Remarks This is a pure kinematical measurement (no dynamics) of the luminosity distance There is a missing component or the stress-energy tensor is not “correct” Possibility 3: The Universe is accelerating The Friedmann equation with pressureless matter does not describe correctly the observations The new fluid must have a negative pressure

Consequences & Remarks This is a pure kinematical measurement (no dynamics) of the luminosity distance There is a missing component or the stress-energy tensor is not “correct” Possibility 3: The Universe is accelerating Possible candidates include … • Cosmological constant • Scalar field (quintessence) • Extented quintessence • K-essence • Chaplygin gas-Quartessence • Bulk viscosity • Super-horizon modes • Quantum cosmological effect • etc … The Friedmann equation with pressureless matter does not describe correctly the observations

Quintessence One postulates the presence of a scalar field Q with a runaway potential and  = 0 If the field is subdominant, there exists a particular solution such that NB: is the equation of state of the background fluid, i.e. 1/3 or 0 The field tracks the background and eventually dominates

Quintessence When the field starts dominating the matter content of the Universe, it leaves the particular solution. This one can be written as This happens for The mass of the field (defined as the second derivative of the potential) is

Quintessence The particular solution is an attractor and is joined for a huge range of initial conditions radiation The attractor is joined matter quintessence The coincidence problem is solved: the acceleration starts recently The attractor is joined

Quintessence The equation of state is a time-dependent (or redshift -dependent) quantity The present value is negative and different from -1. Hence it can be distinguished from a cosmological constant Of course, the present value of the equation of state is also independent from the initial conditions

Quintessence The energy scale M of the potential is fixed by the requirement that the quintessence energy density today represents 70% of the critical energy density Electroweak scale The index  is a free quantity. However,  cannot be too large otherwise the equation of state would be too far from -1 even for the currently available data

Quintessence The evolution of the small inhomogeneities is controlled by the perturbed Klein-Gordon equation WMAP 1 data Clustering of quintessence only on scales of the order of the Hubble radius

High energy physics & Quintessence We address the model-building question in the framework of Super-gravity. The main purpose is to test what should be done in order to produce a satisfactory dark energy model D-term F-term The model is invariant under a group which factorizes as G£ U(1) Fayet-Iliopoulos

High energy physics & Quintessence To go further, one must specify the Kähler and super - potentials in the quintessence sector {Q, X, Y}. A simple expression for W is can be justified if the charges of X, Y and Q under U(1) are 1, -2 and 0 Mass scale: cut-off of the effective theory used There are two important ingredients: no quadratic term in Y, p>1 no direct coupling between X and Q, otherwise the matrix is not diagonal

But how to control terms like with High energy physics & Quintessence After straightforward calculations, the potential reads SUGRA correction This simple estimate leads to different problems ? In some sense, the fine tuning reappears …

High energy physics & Quintessence What are the effects of the SUGRA corrections? 1- The attractor solution still exists since, for large redshifts, the vev of Q is small in comparison with the Planck mass 2- The exponential corrections pushes the equation of state towards -1 at small redshifts 3- The present value of the equation of state becomes “universal”, i.e. does not depend on 

Measuring the (constant) equation of state WMAP1+CBI+ACBAR SUGRA WMAP1+CBI+ACBAR+2dF SNIa 2004

High energy physics & Quintessence mSUGRA SUSY Gravity mediated Inflaton Hidden sector Observable sector Fifth force test, equivalence principle test etc … Quintessence sector

Coupling the inflaton to quintessence The basic assumption is that Q is a test field in a background the evolution of which is controlled by the inflaton  with COBE & WMAP Typically, the quintessence field is frozen during inflation

Inflation Quintessence Coupling the inflaton to quintessence The basic assumption is that Q and the inflaton belong to different sectors of the theory. This means that

Coupling the inflaton to quintessence To go further, a model for (chaotic) inflation is needed. One takes N.B.: Ratra-Peebles/SUGRA N.B.:

Coupling the inflaton to quintessence absolute minimum

Coupling the inflaton to quintessence If the quintessence field is a test field, then Q evolves in an effective time-dependent potential given by Slow-rolling inflaton field The effective potential possesses a time-dependent minimum N.B.: at the minimum, Q is not light

Coupling the inflaton to quintessence The evolution of the minimum is “ adiabatic” The minimum is an attractor The effect of the interaction term is important and keeps Q small during inflation

Conclusions • Quintessence is a model of dark energy where a scalar field is supposed • to be responsible for the accelerated expansion of the Universe. It has • some nice properties like the ability to solve the coincidence problem. • The Quintessence equation of state now is not -1 as for the cosmological • constant and is red-shift dependent. • Quintessence is not clustered on scales smaller than the Hubble radius. • Implementing Quintessence in high energy physics is difficult and no • fully satisfactory model exists at present. • The interaction of Quintessence with the rest of the world is non trivial • and can lead to interesting phenomena and/or constraints.

Quantum effects during inflation The quantum effects in curved space-time can be computed with the formalism of “ stochastic inflation”. Window function Only contains short wavelength modes because of the window function Coarse-grained field, averaged over a Hubble patch: contains long-wavelength modes The window function does not vanish if : “Hubble patch”

Quantum effects during inflation The evolution of the coarse-grained field is controlled by the Langevin equation The coarse-grained field becomes a stochastic process “quantum noise”, sourced by the short wavelength modes “Classical drift” For the free case, one can check that one recovers the standard result : Brownian motion

Quantum effects during inflation The quintessence field during inflation is also controlled by a Langevin equation Quintessence noise Depends on the inflaton noise The solution to this equation allows us to compute the mean value of the Quintessence field N.B.: The inflaton noise does not play an important role

Quantum effects during inflation • The confidence region enlarges with the power index  • A “small” number of total e-foldings is favored

Dark Energy & High-Energy Physics