Constraints on Nonconformal Couplings from the Properties of the Cosmic Microwave Background Radiation

Abstract

Certain modified gravity theories predict the existence of an additional, non-conformally coupled scalar field. A disformal coupling of the field to the Cosmic Microwave Background (CMB) is shown to affect the evolution of the energy density in the radiation fluid and produces a modification of the distribution function of the CMB, which vanishes if photons and baryons couple in the same way to the scalar. We find the constraints on the couplings to matter and photons coming from the measurement of the CMB temperature evolution and from current upper limits on the µ-distortion of the CMB spectrum. We also point out that the measured equation of state of photons differs from wγ = 1/3 in the presence of disformal couplings. PACS numbers:Among the extensions of General Relativity (GR) which have attracted a lot of attention in the literature are scalar-tensor theories, which are also well motivated by some extensions of the standard model such as theories with extra spatial dimensions. In cosmology, those theories have been studied in the context of inflation and models for dark energy as they provide a natural mechanism to drive a period of accelerated expansion in the very early or late universe, see e.g. [1][2][3]. There are some open questions regarding scalar-tensor theories, such as whether the Einstein frame (EF) or Jordan frame (JF) formulation of a given theory is the most "physical", see e.g. [4] and references therein for a discussion.The EF is the frame in which the gravity and scalar sector look like GR plus a scalar field, but matter fields feel a metric which is usually conformally related to the EF metric g µν . In the JF formulation of the theory, matter fields are uncoupled to the scalar, but the spin-2 and spin-0 fields are coupled in a non-trivial way. One could also consider more general transformations of the metric, in which the EF and the JF metrics are not related by a conformal transformation, but a so-called disformal transformation, which includes derivatives of the scalar field (see the definition in Eq. (2) In this paper, we consider scalar-tensor theories with disformally coupled scalar fields and study in particular the consequences on the properties of the CMB. We express observables in terms of the metric a (baryonic) observer feels, to side-step the question about a frameindependent formulation for disformally coupled fields. * Email address: C.vandeBruck@sheffield.ac.uk † Email address: app12jam@sheffield.ac.uk ‡ Email address: Susan.Vu@sheffield.ac.ukFrame-independence in conformally coupled theories has been discussed in [14,15]. The theory we consider is given in the EF aswhere the different matter fields χ i propagate on geodesics for metrics given bỹFrom now on, reduced Planck units are assumed: c = = k B = M Pl = 1. We consider a cosmological setting for eq. (1), where g µν is the standard flat FRW metric, with dsVariation of the action with respect to the fields yields the Klein-Gordon equation for the scalar field φ and the energy conservation equations:where the couplin...

Cosmological tests of the disformal coupling to radiation

“…In this work we focus on what cosmological observations can tell us about the possible existence of disformal scalar fields. This connects with the work in [9], however in that work only the interactions between scalar fields and radiation were studied and all effects of matter were neglected.…”

Beyond the cosmological standard model

“…185], one can more generally assume different couplings to different matter species, thereby explicitly violating the weak equivalence principle. We also ignore the possibility of derivative interactions with matter, such as the disformal screening mechanism [186][187][188][189][190][191]. 10 A trivial way to approximately recover GR is of course to make the scalar-mediated force sufficiently weak on all scales, e.g., by making the coupling of ϕ to matter, g, to be very small universally.…”

Transforming gravity: From derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian

“…Disformal relations also appear in generalized Palatini gravities [62], provide new symmetries of Maxwell's [63] and Horndeski's [33] theories, allow for the Lorentzian signature of the metric to emerge dynamically [64,65] and might be used in the construction of renormalizable theories of gravity [66]. Unlike conformal relations, disformal couplings have non-trivial effects on radiation and can affect photons, a possibility that has been studied in the context of laboratory tests [67] and cosmological implications [68][69][70].…”