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

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, (2005), astro-ph/ P. Brax & J. Martin, Phys. Lett. B, 40 (1999), astro-ph/ P. Brax & J. Martin, Phys. Rev. D 61, (2000), astro-ph/ P. Brax, J. Martin & A. Riazuelo, Phys. Rev. D 62, (2000), astro-ph/ P. Brax, J. Martin & A. Riazuelo, Phys. Rev. D 64, (2001), hep-ph/ J. Martin & M. Musso, Phys. Rev. D, to appear, astro-ph/

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

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 [J. L. Tonry et al., Astrophys. J 594, 1 (2003), astro-ph/ ] [W. Freedman & M. Turner, Rev. Mod. Phys. 75, 1433 (2003), astro-ph/ ]

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

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 Possibility 1: The observations are not correct, e.g. the SNIa are not standard candels (dust, evolution etc …)

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 Possibility 2: Gravity is modified New “large” characteristic scale

There is a missing component or the stress-energy tensor is not “correct” 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 Possibility 3: Possible candidates include … Cosmological constant Scalar field (quintessence) Extented quintessence K-essence Chaplygin gas-Quartessence Bulk viscosity Super-horizon modes Quantum cosmological effect etc …

There is a missing component or the stress-energy tensor is not “correct” 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 Possibility 3: The new fluid must have a negative pressure

There is a missing component or the stress-energy tensor is not “correct” 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 Possibility 3: Possible candidates include … Cosmological constant Scalar field (quintessence) Extented quintessence K-essence Chaplygin gas-Quartessence Bulk viscosity Super-horizon modes Quantum cosmological effect etc …

There is a missing component or the stress-energy tensor is not “correct” 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 Possibility 3: Possible candidates include … Cosmological constant Scalar field (quintessence) Extented quintessence K-essence Chaplygin gas-Quartessence Bulk viscosity Super-horizon modes Quantum cosmological effect etc …

There is a missing component or the stress-energy tensor is not “correct” 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 Possibility 3: Possible candidates include … Cosmological constant Scalar field (quintessence) Extented quintessence K-essence Chaplygin gas-Quartessence Bulk viscosity Super-horizon modes Quantum cosmological effect etc …

There is a missing component or the stress-energy tensor is not “correct” 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 Possibility 3: Possible candidates include … Cosmological constant Scalar field (quintessence) Extented quintessence K-essence Chaplygin gas-Quartessence Bulk viscosity Super-horizon modes Quantum cosmological effect etc …

There is a missing component or the stress-energy tensor is not “correct” 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 Possibility 3: Possible candidates include … Cosmological constant Scalar field (quintessence) Extented quintessence K-essence Chaplygin gas-Quartessence Bulk viscosity Super-horizon modes Quantum cosmological effect etc …

There is a missing component or the stress-energy tensor is not “correct” 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 Possibility 3: Possible candidates include … Cosmological constant Scalar field (quintessence) Extented quintessence K-essence Chaplygin gas-Quartessence Bulk viscosity Super-horizon modes Quantum cosmological effect etc …

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

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

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

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

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 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 Electroweak scale

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

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 F-term D-term The model is invariant under a group which factorizes as G £ U(1) Fayet-Iliopoulos

To go further, one must specify the Kähler and super - potentials in the quintessence sector {Q, X, Y}. A simple expression for W is 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 can be justified if the charges of X, Y and Q under U(1) are 1, -2 and 0

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

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

SNIa 2004 WMAP1+CBI+ACBAR WMAP1+CBI+ACBAR+2dF SUGRA

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

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

The basic assumption is that Q and the inflaton belong to different sectors of the theory. This means that InflationQuintessence

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

absolute minimum

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

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

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.

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

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

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

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