NCTS Annual Theory Meeting December 2015 Recent status

NCTS Annual Theory Meeting, December, 2015 Recent status of dark energy and beyond Shinji Tsujikawa (Tokyo University of Science)

Observational evidence of dark energy Observations showed that about 70 % of the today’s energy density is dark energy responsible for the cosmic acceleration. 1. Supernovae type Ia (SN Ia) 2. Cosmic Microwave Background (CMB) 3. Baryon Acoustic Oscillations (BAO) The cosmic expansion history is constrained. 4. Large-scale structure (LSS) 5. Weak lensing The evolution of matter perturbations is constrained. This is especially important for modified gravity models.

Today’s cosmic recipe: joint analysis of CMB and other data Main source for structure formation. Gravitational attraction occurs. Responsible for cosmic acceleration Negative pressure

Planck constraints on dark energy in the flat FLRW Universe Equation of state: Marginalized posterior distribution for the constant equation of state For the flat FLRW the bounds are

Constraints on time-varying dark energy equation of state (CPL parametrization) Reconstruction on the DE equation of state We have to caution that the CPL parametrization is not enough to deal with the models with fast-varying equations of state.

Dark energy candidates l The simplest candidate: Cosmological constant Equation of state If the cosmological constant originates from the vacuum energy, its energy scale is enormously larger than the dark energy scale. l Dynamical dark energy models Quintessence, k-essence, chaplygin gas, coupled dark energy, f (R) gravity, scalar-tensor theories, DGP model, Galileon, massive gravity, Lorentz violating model… l Apparent acceleration Difficult to be compatible with observations Inhomogeneous models, metric backreaction

Dynamical dark energy models 1. Modified matter models e. g. Dilatonic ghost condensate: 2. Modified gravity models Such as

Most general single-field scalar-tensor theories with second-order equations of motion (Horndeski theories) Horndeski (1974) Deffayet et al (2011) Charmousis et al (2011) Kobayashi et al (2011) This action covers most of the dark energy models proposed in literature. l Cosmological constant: l Quintessence and K-essence: l f(R) gravity and scalar-tensor gravity: l Galileon: l Gauss-Bonnet coupling :

Friedmann equations in Horndeski theories __ The background equations of motion are __ (Horndeski’s action) Non-relativistic Radiation matter The equation of state of dark energy is given by

Dark energy equation of state: modified matter models (1) LCDM (2) Quintessence (a) Freezing models (b) Thawing models . . (3) k-essence e. g. PNGB boson

Quintessence: Theory and Observations Theoretical prediction Observational constraints for l The freezing model is in high tension with the data. l The thawing model is allowed, but it is not particularly favored over the LCDM.

Modified gravity allows w smaller than -1. f(R) model: Hu and Sawicki, Starobinsky (2007) Galileons: l f(R) model is consistent with the data. l For Galileons, only late-time tracking solutions are allowed from the data. Tracking solutions of Galileons are disfavored from the data.

Constraints from the growth history of the Universe Dark energy models can be further distinguished from the growth of structures, e. g. , large-scale structure, weak lensing, CMB etc. In doing so, we need to study the evolution of cosmological perturbations. LSS Weak lensing Perturbed metric: Non-relativistic matter: with the four velocity CMB

Growth of structures in General Relativity (including Lambda, quintessence, k-essence) (Newton’s gravitational constant) In the matter era, there is the growing-mode solution In the dark energy dominated epoch, the growth rate is smaller. For the models in the framework of GR, the difference between models is small.

Planck constraints on the effective gravitational coupling and the gravitational slip parameter (Ade et al, 2015) today Strong gravity Weak gravity GR today

Weak gravity ? The recent observations of redshift-space distortions (RSD) measured the lower growth rate of matter perturbations lower than that predicted by the LCDM model. Macaulay et al, PRL (2014) Planck LCDM fit Tension between Planck and RSD data RSD fit

Cosmic growth rate in Horndeski theories In the observations of redshift space distortions (RSD), the growth rate of matter perturbations is constrained from peculiar velocities of galaxies. The gauge-invariant density contrast ___ obeys where

Effective gravitational coupling in Horndeski theories De Felice, Kobayashi, S. T. (2011). Schematically The effect of modified gravity manifests itself.

Simple form of the effective gravitational coupling ST (2015) In the massless limit, the effective gravitational coupling in Horndeski theories reads ____ Tensor contribution This correspond to the intrinsic modification of the gravitational part. _______ Scalar contribution Always positive under the no-ghost and no-instability conditions: The necessary condition to realize weaker gravity than that in GR is The scalar-matter interaction always enhances the effective gravitational coupling.

Examples Hu and Sawicki, Starobinsky, ST. (i) f(R) gravity: (ii) Covariant Galileons Deffayet et al. De Felice, Kase, ST (2011)

Latest constraints from redshift space distortion measurements Okumura et al. , ar. Xiv: 1511. 08083 New data from Fast. Sound The strong gravity models like covariant Galileons are disfavored from the data.

Summary of the current status of dark energy and beyond 1. The cosmological constant is consistent with the data of background, but it shows interesting tension between high-redshift (CMB) and low-redshift (RSD) data. 2. There is no strong evidence that modified matter models with w>-1 (quintessence) are favored over the cosmological constant. 3. Modified gravity models can explain w<-1 consistent with observations. The strong gravity model like Galileons are in tension with the RSD data. In the near future we should clarify the following two issues.