Physics Letters B 794 (2019) 135–142
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Physics Letters B
www.elsevier.com/locate/physletb
Massive mimetic cosmology
Adam R. Solomon
a,∗
, Valeri Vardanyan
b,c
, Yashar Akrami
d,b
a
Department of Physics & McWilliams Center for Cosmology, Carnegie Mellon University, Pittsburgh, PA 15213, USA
b
Lorentz Institute for Theoretical Physics, Leiden University, P.O. Box 9506, 2300 RA Leiden, the Netherlands
c
Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, the Netherlands
d
Département de Physique, École Normale Supérieure, PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France
a r t i c l e i n f o a b s t r a c t
Article history:
Received
14 March 2019
Received
in revised form 24 May 2019
Accepted
28 May 2019
Available
online 30 May 2019
Editor:
H. Peiris
We study the first cosmological implications of the mimetic theory of massive gravity recently proposed
by Chamseddine and Mukhanov. This is a novel theory of ghost-free massive gravity which additionally
contains a mimetic dark matter component. In an echo of other modified gravity theories, there are self-
accelerating
solutions which contain a ghost instability. In the ghost-free region of parameter space, the
effect of the graviton mass on the cosmic expansion history amounts to an effective negative cosmological
constant, a radiation component, and a negative curvature term. This allows us to place constraints on the
model parameters—the graviton mass and the Stückelberg vacuum expectation value—by insisting that
the effective radiation and curvature terms be within observational bounds. The late-time acceleration
must be accounted for by a separate positive cosmological constant or other dark energy sector. We
impose further constraints at the level of perturbations by demanding linear stability. We comment on
the possibility of distinguishing this theory from CDM with current and future large-scale structure
surveys.
© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Chamseddine and Mukhanov have recently proposed [1,2]a
novel ghost-free theory of massive gravity in which one of the
four Stückelberg scalars is constrained in the same way as in the
mimetic theory of dark matter [3], spontaneously breaking Lorentz
invariance. In this Letter, we study the immediate implications of
this mimetic massive gravity for cosmological theory and observa-
tion.
From
a field-theoretic perspective, general relativity is the
unique theory (in four spacetime dimensions) of a massless spin-
2
particle, or graviton. It is therefore natural to ask whether it is
possible to endow the graviton with a non-zero mass, and what
sort of theoretical structures would result [4]. A closely related
line of inquiry asks whether it is possible for two or more gravi-
tons
to interact [5]. Most nonlinear realizations of such theories
suffer from the so-called Boulware-Deser ghost instability [6]. The
past decade has seen the construction of models which avoid this
instability, allowing for the construction of ghost-free theories of
*
Corresponding author.
E-mail
addresses: adamsolo@andrew.cmu.edu (A.R. Solomon),
vardanyan@lorentz.leidenuniv.nl (V. Vardanyan), akrami@ens.fr (Y. Akrami).
massive gravity [7–13] and bimetric and multimetric gravity [12,
14,15].
We refer the reader to the reviews [16,17]on massive grav-
ity
and [18,19]on bimetric gravity. The theory of mimetic massive
gravity proposed in Refs. [1,2]takes a new and alternative path to
a ghost-free nonlinear theory of massive gravity.
A
generic theory of massive gravity propagates six degrees of
freedom, which should be thought of as the five helicity states of
a massive graviton plus an additional, ghostly scalar. The easiest
way to understand the degrees-of-freedom counting is to observe
that a graviton mass breaks diffeomorphism invariance. This is a
gauge symmetry and so can be restored by the addition of four
Stückelberg scalars
A
, which propagate in addition to the two
(now potentially massive) tensor modes of general relativity.
As
an illustration, consider a Lorentz-invariant theory of mas-
sive
gravity. In order to construct non-trivial, non-derivative inter-
actions
for the metric, one requires a second “reference” metric.
The simplest choice for this metric is that of flat space, η
μν
, but
the addition of this prior geometry breaks diffeomorphism invari-
ance;
for instance, there are preferred coordinate systems in which
η
μν
= diag(−1, 1, 1, 1). But diffeomorphism invariance is simply
a redundancy in description, and can be restored by the addi-
tion
of redundant variables, i.e., replacing η
μν
→ η
AB
∂
μ
A
∂
ν
B
,
where η
AB
= diag(−1, 1, 1, 1) and the four fields
A
transform as
https://doi.org/10.1016/j.physletb.2019.05.045
0370-2693/
© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.