Linear perturbation theory and structure formation in a Brans-Dicke theory of gravity without dark matter

TL;DR

This paper explores a scalar-tensor gravity theory without dark matter that can explain galaxy dynamics and cosmic acceleration, but faces challenges in early structure formation consistent with observations.

Contribution

It analyzes a specific Brans-Dicke scalar-tensor model's implications for structure formation and cosmic acceleration without dark matter or dark energy.

Findings

Delayed structure formation at low redshift contradicts observations

Scalar field enhances gravity differently for particles and photons

Potential for alternative models to address early universe structure growth

Abstract

We investigate the formation of the large-scale cosmic structure in a scalar-tensor theory of gravity belonging to the class of the Brans--Dicke theories. The universe contains baryonic matter alone and neither dark matter nor dark energy. The two arbitrary functions of the scalar field characterizing the kinetic term and the self-interaction potential are set to $W(\varphi)=-1$ and $V(\varphi) = -\Xi \varphi$, respectively, with $\Xi$ a positive constant. In the weak-field limit, the theory reduces to Refracted Gravity, a non-relativistic theory whose modified Poisson equation contains the scalar field $\varphi$ that provides the gravitational boost required to describe the dynamics of galaxies and galaxy clusters without dark matter. In a flat, matter-dominated, homogeneous and isotropic universe the same scalar field $\varphi$ drives the accelerated expansion of the universe and describes the observed redshift evolution of the Hubble-Lema\^itre parameter $H(z)$. However, in the equation of the growth factor of the linear perturbation theory, the form of $V(\varphi)$ makes the coefficient of the source of the gravitational field proportional to $H^{-1}(z)$; therefore the gravitational field is strongly suppressed at early times and structure formation is delayed to redshift $z< 1$, in disagreement with the observation of formed galaxies at much larger redshifts. In addition, the form of $W(\varphi)$ and a linear $V(\varphi)$ imply that $\varphi$ generates twice the gravitational boost on massive particles than on photons, with possible observable consequences on the gravitational lensing phenomenon. It remains to be investigated whether different choices of $W(\varphi)$ and $V(\varphi)$, that can still make the theory reduce to Refracted Gravity in the weak-field limit, might alleviate these problems.