Brax, Philippe
Cespedes, Sebastian
Davis, Anne-Christine

The impact of the existence of gravitons with non-vanishing masses on the B-modes of the Cosmic Microwave Background (CMB) is investigated. We also focus on putative modifications to the speed of the gravitational waves. We find that a change of the graviton speed shifts the acoustic peaks of the CMB and then could be easily constrained. For the case of massive gravity, we show analytically how the B-modes are sourced in a manner differing from the massless case leading to a plateau at low l in the CMB spectrum. We also study the case when there are more than one graviton, and when pressure instabilities are present. The latter would occur in doubly coupled bigravity in the radiation era. We focus on the case where a massless graviton becomes tachyonic in the radiation era whilst a massive one remains stable. As the unstable mode decouples from matter in the radiation era, we find that the effects of the instability is largely reduced on the spectrum of B-modes as long as the unstable graviton does not grow into the non-linear regime. In all cases when both massless and massive gravitons are present, we find that the B-mode CMB spectrum is characterised by a low l plateau together with a shifted position for the first few peaks compared to a purely massive graviton spectrum, a shift which depends on the mixing between the gravitons in their coupling to matter and could serve as a hint in favour of the existence of multiple gravitons.

Naik, Aneesh P.
Puchwein, Ewald
Davis, Anne-Christine
Arnold, Christian

Current constraints on gravity are relatively weak on galactic and intergalactic scales. Screened modified gravity models can exhibit complex behaviour there without violating stringent tests of gravity within our Solar System. They might hence provide viable extensions of the theory of gravity. Here, we use galaxy kinematics to constrain screened modified gravity models. We focus on chameleon f(R) gravity and predict its impact on galaxy rotation curves and radial acceleration relations. This is achieved by post-processing state-of-the-art galaxy formation simulations from the AURIGA PROJECT, using the MG-GADGET code. For a given galaxy, the surface dividing screened and un-screened regions adopts an oblate shape, reflecting the disc morphology of the galaxy's mass distribution. At the 'screening radius' - the radius at which screening is triggered in the disc plane - characteristic 'upturns' are present in both rotation curves and radial acceleration relations. The locations of these features depend on various factors, such as the galaxy mass, the concentration of the density profile, and the value of the background field amplitude (f) over bar Ro. Self-screening of stars and environmental screening also play a role. For Milky Way-size galaxies, we find that a model with vertical bar(f) over bar (R0)vertical bar =3D 10(-7) results in rotation curves that are indistinguishable from ACDM, while for vertical bar(f) over bar (R0)vertical bar >=3D 2 x 10(-6) the simulated galaxies are entirely unscreened, violating Solar System constraints. For intermediate values, distinct upturns are present. With a careful statistical analysis of existing samples of observed rotation curves, including lower mass objects, constraints on f(R) gravity with a sensitivity down to vertical bar(f) over bar (R0)vertical bar similar to 10(-7) should be possible.

Brax, Philippe
Burrage, Clare
Davis, Anne-Christine

We review laboratory constraints on theories of modified gravity and show that they are complementary to cosmological and astrophysical tests. We particularly focus on the environmentally dependent. dilaton, as a worked example to show how such constraints are derived. Finally we discuss precision photons experiments, and why these may also give us information about possible modifications of gravity.

Brax, Philippe
Davis, Anne-Christine
Noller, Johannes

We analyse the late time cosmology and the gravitational properties of doubly coupled bigravity in the constrained vielbein formalism (equivalent to the metric formalism) when the mass of the massive graviton is of the order of the present Hubble rate. We focus on one of the two branches of background cosmology where the ratio between the scale factors of the two metrics is algebraically determined. We find that the late time physics depends on the mass of the graviton, which dictates the future asymptotic cosmological constant. The Universe evolves from a matter dominated epoch to a dark energy dominated era where the equation of state of dark energy can always be made close to -1 now by appropriately tuning the graviton mass. We also analyse the perturbative spectrum of the theory in the quasi-static approximation, well below the strong coupling scale where no instability is present, and we show that there are five scalar degrees of freedom, two vectors and two gravitons. In Minkowski space, where the four Newtonian potentials vanish, the theory manifestly reduces to one massive and one massless graviton. In a cosmological FRW background for both metrics, four of the five scalars are Newtonian potentials which lead to a modification of gravity on large scales. The fifth one gives rise to a ghost which decouples from pressure-less matter in the quasi-static approximation. In this scalar sector, gravity is modified with effects on both the growth of structure and the lensing potential. In particular, we find that the Sigma parameter governing the Poisson equation of the weak lensing potential can differ from one in the recent past of the Universe. Overall, the nature of the modification of gravity at low energy, which reveals itself in the growth of structure and the lensing potential, is intrinsically dependent on the couplings to matter and the potential term of the vielbeins. We also find that the time variation of Newton's constant in the Jordan frame can easily satisfy the bound from solar system tests of gravity. Finally we show that the two gravitons present in the spectrum have a nontrivial mass matrix whose origin follows from the potential term of bigravity. This mixing leads to gravitational birefringence.

We present a novel way to investigate scalar field pro files around black holes with an accretion disc for a range of models where the Compton wavelength of the scalar is large compared to other length scales. By analysing the problem in "Weyl" coordinates, we are able to calculate the scalar pro files for accretion discs in the static Schwarzschild, as well as rotating Kerr, black holes. We comment on observational effects.

Burrage, Clare
Cespedes, Sebastian
Davis, Anne-Christine

Inthis work we study the role of disformal transformation on cosmological backgrounds and its relation to the speed of sound for tensor modes. A speed different from one for tensor modes can arise in several contexts, such as Galileons theories or massive gravity, nevertheless the speed is very constrained to be one by observations of gravitational wave emission. It has been shown that in inflation a disformal transformation allows to set the speed for tensor modes to one without making changes to the curvature power spectrum. Here we show that this invariance does not hold when considering the CMS anisotropy power spectrum. It turns out that the after doing the transformation there is an imprint on the acoustic peaks and the diffusion damping. This has interesting consequences; here we explore quartic galileon theories which allow a modified speed for tensor modes. For these theories the transformation can be used to constraint the parameter space in different regimes.

Brax, Philippe
Burrage, Clare
Davis, Anne-Christine

We analyse the speed of gravitational waves in coupled Galileon models with an equation of state omega(phi) =3D -1 now and a ghost-free Minkowski limit. We find that the gravitational waves propagate much faster than the speed of light unless these models are small perturbations of cubic Galileons and the Galileon energy density is sub-dominant to a dominant cosmological constant. In this case, the binary pulsar bounds on the speed of gravitational waves can be satisfied and the equation of state can be close to -1 when the coupling to matter and the coefficient of the cubic term of the Galileon Lagrangian are related. This severely restricts the allowed cosmological behaviour of Galileon models and we are forced to conclude that Galileons with a stable Minkowski limit cannot account for the observed acceleration of the expansion of the universe on their own. Moreover any subdominant Galileon component of our universe must be dominated by the cubic term. For such models with gravitons propagating faster than the speed of light, the gravitons become potentially unstable and could decay into photon pairs. They could also emit photons by Cerenkov radiation. We show that the decay rate of such speedy gravitons into photons and the Cerenkov radiation are in fact negligible. Moreover the time delay between the gravitational signal and light emitted by explosive astrophysical events could serve as a confirmation that a modification of gravity acts on the largest scales of the Universe.

Modified gravity models with screening in local environments appear in three different guises: chameleon, K-mouflage and Vainshtein mechanisms. We propose to look for differences between these classes of models by considering cosmological observations at low redshift. In particular, we analyse the redshift dependence of the fine structure constant and the proton to electron mass ratio in each of these scenarios. When the absorption lines belong to unscreened regions of space such as dwarf galaxies, a time variation would be present for chameleons. For both K-mouflage and Vainshtein mechanisms, the cosmological time variation of the scalar field is not suppressed in both unscreened and screened environments, therefore enhancing the variation of constants and their detection prospect. We also consider the time variation of the redshift of distant objects using their spectrocopic velocities. We find that models of the K-mouflage and Vainshtein types have very different spectroscopic velocities as a function of redshift and that their differences with the Lambda-CDM template should be within reach of the future ELT-HIRES observations.

We formulate new conformal models of inflation and dark energy which generalise the Higgs-Dilaton scenario. We embed these models in unimodular gravity whose effect is to break scale invariance in the late time Universe. In the early Universe, inflation occurs close to a maximum of both the scalar potential and the scalar coupling to the Ricci scalar in the Jordan frame. At late times, the dilaton, which decouples from the dynamics during inflation, receives a potential term from unimodular gravity and leads to the acceleration of the Universe. We address two central issues in this scenario. First we show that the Damour-Polyalov mechanism, when non-relativistic matter is present prior to the start of inflation, sets the initial conditions for inflation at the maximum of the scalar potential. We then show that conformal invariance implies that matter particles are not coupled to the dilaton in the late Universe at the classical level. When fermions acquire masses at low energy, scale invariance is broken and quantum corrections induce a coupling between the dilaton and matter which is still small enough to evade the gravitational constraints in the solar system.

Brax, Philippe
Davis, Anne-Christine
Li, Baojiu
Winther, Hans A.
Zhao, Gong-Bo

In this work we systematically study the linear and nonlinear structure formation in chameleon theories of modified gravity, using a generic parameterisation which describes a large class of models using only 4 parameters. For this we have modified the N-body simulation code ECOSMOG to perform a total of 65 simulations for different models and parameter values, including the default Lambda CDM. These simulations enable us to explore a significant portion of the parameter space. We have studied the effects of modified gravity on the matter power spectrum and mass function, and found a rich and interesting phenomenology where the difference with the Lambda CDM paradigm cannot be reproduced by a linear analysis even on scales as large as k similar to 0.05 hMpc(-1), since the latter incorrectly assumes that the modification of gravity depends only on the background matter density. Our results show that the chameleon screening mechanism is significantly more efficient than other mechanisms such as the dilaton and symmetron, especially in high-density regions and at early times, and can serve as a guidance to determine the parts of the chameleon parameter space which are cosmologically interesting and thus merit further studies in the future.

Brax, Philippe
Davis, Anne-Christine
Sakstein, Jeremy

We investigate the cosmological dynamics of a class of supersymmetric chameleon models coupled to cold dark matter fermions. The model includes a cosmological constant in the form of a Fayet-Illiopoulos term, which emerges at late times due to the coupling of the chameleon to two charged scalars. Supergravity corrections ensure that the supersymmetric chameleons are efficiently screened in all astrophysical objects of interest, however this does not preclude the enhancement of gravity on linear cosmological scales. We solve the modified equations for the growth of cold dark matter density perturbations in closed form in the matter era. Using this, we go on to derive the modified linear power spectrum which is characterised by two scales, the horizon size at matter-radiation equality and at the redshift when the chameleon reaches the minimum of its effective potential. We analyse the deviations from the ACDM predictions in the linear regime. We find that there is generically a region in the model's parameter space where the model's background cosmology coincides with that of the ACDM model. Furthermore, we find that characteristic deviations from ACDM are present on the matter power spectrum providing a clear signature of supersymmetric chameleons.

Avgoustidis, Anastasios
Cremonini, Sera
Davis, Anne-Christine
Ribeiro, Raquel H.
Turzynski, Krzysztof
Watson, Scott

We re-examine the importance of slow-roll corrections during the evolution of cosmological perturbations in models of multi-field inflation. We find that in many instances the presence of light degrees of freedom leads to situations in which next to leading order slow-roll corrections become significant. Examples where we expect such corrections to be crucial include models in which modes exit the Hubble radius while the inflationary trajectory undergoes an abrupt turn in field space, or during a phase transition. We illustrate this with several examples hybrid inflation, double quadratic inflation and double quartic inflation. Utilizing both analytic estimates and full numerical results, we find that corrections can be as large as 20%. Our results have implications for many existing models in the literature, as these corrections must be included to obtain accurate observational predictions - particularly given the level of accuracy expected from CMB experiments such as Planck.

Davis, Anne-Christine
Li, Baojiu
Mota, David F.
Winther, Hans A.

Scalar fields, strongly coupled to matter, can be present in nature and still be invisible to local experiments if they are subject to a screening mechanism. The symmetron is one such mechanism that relies on restoration of a spontaneously broken symmetry in regions of high density to shield the scalar fifth force. We have investigated structure formation in the symmetron model by using N-body simulations and find observable signatures in both the linear and nonlinear matter power spectrum and on the halo mass function. The mechanism for suppressing the scalar fifth force in high-density regions is also found to work very well.

Davis, Anne-Christine
Lim, Eugene A.
Sakstein, Jeremy
Shaw, Douglas J.

We investigate the effect of modified gravity with screening mechanisms, such as the chameleon or symmetron models, upon the structure of main sequence stars. We find that unscreened stars can be significantly more luminous and ephemeral than their screened doppelgangers. By embedding these stars into dwarf galaxies, which can be unscreened for values of the parameters not yet ruled out observationally, we show that the cumulative effect of their increased luminosity can enhance the total galactic luminosity. We estimate this enhancement and find that it can be considerable given model parameters that are still under experimental scrutiny. By looking for systematic offsets between screened dwarf galaxies in clusters and unscreened galaxies in voids, these effects could form the basis of an independent observational test that can potentially lower the current experimental bounds on the model independent parameters of these theories by an order of magnitude or more.

Davis, Anne-Christine
Li, Baojiu
Mota, David F.
Winther, Hans A.

Scalar fields, strongly coupled to matter, can be present in nature and still be invisible to local experiments if they are subject to a screening mechanism. The symmetron is one such mechanism that relies on restoration of a spontaneously broken symmetry in regions of high density to shield the scalar fifth force. We have investigated structure formation in the symmetron model by using N-body simulations and find observable signatures in both the linear and nonlinear matter power spectrum and on the halo mass function. The mechanism for suppressing the scalar fifth force in high-density regions is also found to work very well.