Physics Letters B 796 (2019) 112–116
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Primordial bouncing cosmology in the Deser-Woodard nonlocal gravity
Che-Yu Chen
a,b,∗
, Pisin Chen
a,b,c
, Sohyun Park
d
a
Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan
b
LeCosPA, National Taiwan University, Taipei 10617, Taiwan
c
Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94305, USA
d
CEICO, Institute of Physics of the Czech Academy of Sciences, Na Slovance 2, 18221 Prague 8, Czech Republic
a r t i c l e i n f o a b s t r a c t
Article history:
Received
11 May 2019
Received
in revised form 8 July 2019
Accepted
11 July 2019
Available
online 15 July 2019
Editor: J.
Hisano
Keywords:
Modified
theories of gravity
Bouncing
cosmology
Nonlocal
gravity
The Deser-Woodard (DW) nonlocal gravity model has been proposed in order to describe the late-time
acceleration of the universe without introducing dark energy. In this paper we focus, however, on the
early stage of the universe and demonstrate how a primordial bounce in the vacuum spacetime can be
realized in the framework of the DW nonlocal model. We reconstruct the nonlocal distortion function,
which encodes all the modifications to the Einstein-Hilbert action, in order to generate bouncing solutions
to solve the initial singularity problem. We show that the initial conditions can be chosen in such a way
that the distortion function and its first order derivative approach zero after the bounce and the standard
cosmological solution described by general relativity is recovered afterwards. We also study the evolution
of anisotropies near the bounce. It turns out that the shear density defined by the anisotropy grows
towards the bounce, but due to the presence of nonlocal effects, it grows in a milder manner compared
with that in Einstein gravity.
© 2019 The Author(s). 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
One of the fundamental problems in Einstein’s general relativ-
ity
(GR) is the existence of spacetime singularities associated with
the energy conditions for matter fields. The definition of space-
time
singularities in the notion of geodesic incompleteness in GR
has been established by Hawking and Penrose [1]. In the standard
big bang cosmology, the universe started with a big bang singu-
larity,
at which the spacetime curvature diverges, jeopardizing the
applicability of GR at the initial time.
It
has been suggested that the big bang singularity can be re-
placed
by a nonsingular bouncing scenario in which all curvature
invariants become finite. In fact, such bouncing cosmologies have
been realized in the context of loop quantum cosmology [2,3]and
string theory [4]. In practice, one can either construct bouncing
solutions within the framework of GR by introducing matter fields
which violate null energy conditions [5–7], or modify GR such that
bouncing solutions can be obtained without violating any energy
conditions [8–17]. See Ref. [18] and the references therein for a
review.
*
Corresponding author .
E-mail
addresses: b97202056@gmail.com (C.-Y. Chen),
pisinchen@phys.ntu.edu.tw (P. Chen), park@fzu.cz (S. Park).
A nonlocal addition to GR is motivated by the fact that quan-
tum
loops of massless particles such as gravitons inevitably give
rise to nonlocal quantum corrections, see for example [19]. It has
been noted that a nonlocal quantum effective action might be
obtained from a fundamental local Lagrangian through the gravita-
tional
vacuum polarization of infrared gravitons [20,21]. However,
such a derivation from first principles is not yet available, there-
fore
a compromised approach has been to construct a nonlocal
effective action with an aim to describe phenomena that cannot be
explained by GR with ordinary matter. Nonlocal models replacing
dark matter, sometimes called the nonlocal metric realization of
MOND (MOdified Newtonian Dynamics), have also been proposed
and studied in Ref. [22–28]. For the nonlocal models that attempt
to explain inflation, see Refs. [29–34].
So
far the most popular application of nonlocal gravity has been
the late-time cosmic acceleration without dark energy [35–44].
Among such models, the two most studied are the Deser-Woodard
(DW) model [36], which distorts the Ricci scalar R by a function
of the nonlocal dimensionless scalar
−1
R, and the Maggiore-
Mancarella
(MM) model [41], which introduces a mass parame-
ter
m
2
multiplied by the dimensionful nonlocal scalar
−2
R. For
the DW model, cosmological perturbations and structure forma-
tion
have been studied in Refs. [46–51]. The issues concerning
causality, localization, degrees of freedom and stability [52–56],
and the gravitational energy-momentum flux due to an isolated
https://doi.org/10.1016/j.physletb.2019.07.024
0370-2693/
© 2019 The Author(s). 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
.