Physics Letters B 797 (2019) 134901
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Cosmological constant: Relaxation vs multiverse
Alessandro Strumia
a
, Daniele Teresi
a,b,∗
a
Dipartimento di Fisica “E. Fermi”, Università di Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy
b
INFN, Sezione di Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy
a r t i c l e i n f o a b s t r a c t
Article history:
Received
18 June 2019
Received
in revised form 21 August 2019
Accepted
27 August 2019
Available
online 30 August 2019
Editor:
G.F. Giudice
Keywords:
Cosmological
constant
Relaxation
Multiverse
We consider a scalar field with a bottom-less potential, such as g
3
φ, finding that cosmologies unavoidably
end up with a crunch, late enough to be compatible with observations if g 1.2H
2/3
0
M
1/3
Pl
. If rebounces
avoid singularities, the multiverse acquires new features; in particular probabilities avoid some of the
usual ambiguities. If rebounces change the vacuum energy by a small enough amount, this dynamics
selects a small vacuum energy and becomes the most likely source of universes with anthropically small
cosmological constant. Its probability distribution could avoid the gap by 2 orders of magnitude that
seems left by standard anthropic selection.
© 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
The vacuum energy V that controls the cosmological constant
receives power-divergent quantum corrections as well as physi-
cal
corrections of order M
4
max
, where M
max
is the mass of the
heaviest particle. In models with new physics at the Planck scale
(e.g. string theory) one thereby expects Planckian vacuum ener-
gies,
and the observed cosmological constant (corresponding to
the vacuum energy V
0
≈ (2.3 meV)
4
) can be obtained from a can-
cellation
by one part in M
4
Pl
/V
0
∼ 10
120
. In tentative models of
dimensionless gravity the heaviest particle might be the top quark
(M
max
∼ M
t
, see e.g. [1]), still needing a cancellation by one part
in M
4
max
/V
0
∼ 10
60
.
A
plausible interpretation of this huge cancellation is provided
by theories with enough vacua such that at least one vacuum
accidentally has the small observed cosmological constant. Then,
assuming that the vacua get populated e.g. by eternal inflation, ob-
servers
can only develop in those vacua with V 10
3
V
0
[2](see
also [3]). More quantitative attempts of understanding anthropic
selection find that the most likely vacuum energy measured by a
random observer is about 100 times larger that the vacuum energy
V
0
we observe [2,4–6](unless some special measure is adopted,
for instance as in [7–10]). This mild remaining discrepancy might
signal some missing piece of the puzzle.
*
Corresponding author.
E-mail
addresses: alessandro.strumia@unipi.it (A. Strumia),
daniele.teresi@df.unipi.it (D. Teresi).
Recently [11](see also [12]) proposed a cosmological model
that could make the cosmological constant partially smaller and
negative. It needs two main ingredients:
a) ‘Rolling’:
a scalar field φ with a quasi-flat potential and no bot-
tom
(at least in the field space probed cosmologically), such as
V
φ
=−g
3
φ with small g H
2/3
0
M
1/3
Pl
where H
0
is the present
Hubble constant.
Then,
a cosmological phase during which the energy density is
dominated by V
φ
(with a value such that φ classically rolls down
its potential) ends up when V
φ
crosses zero and becomes slightly
negative, starting contraction. During the contraction phase the
kinetic energy of φ rapidly blue-shifts and, assuming some inter-
action
with extra states, gets converted into a radiation bath, thus
reheating the Universe and maybe triggering the following dynam-
ics.
b) ‘Rebouncing’:
a mechanism that turns a contracting universe
into an expanding universe. Furthermore, to get a small posi-
tive
(rather than negative) cosmological constant, the authors
of [11] assume multiple minima and a ‘hiccupping’ mechanism
that populates vacua up to some energy density V
rebounce
.
Hence,
at this stage the Universe appears as hot, expanding and
with a small positive cosmological constant, i.e. with standard hot
Big-Bang cosmology. In this way, the cancellation needed to get
the observed cosmological constant gets partially reduced by some
https://doi.org/10.1016/j.physletb.2019.134901
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
.