Generalized perturbations in modified gravity and dark energy

213 Pages·2014·3.245 MB·English

by  Jonathan Pearson (auth.)

Springer Theses
Recognizing Outstanding Ph.D. Research
Jonathan Pearson
Generalized
Perturbations in
Modified Gravity
and Dark Energy
Springer Theses
Recognizing Outstanding Ph.D. Research
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Jonathan Pearson
Generalized Perturbations
in Modified Gravity
and Dark Energy
Doctoral Thesis accepted by
the University of Manchester, UK
123
Author Supervisor
Dr. Jonathan Pearson Prof.Richard Battye
Department of Mathematical Sciences School ofPhysicsand Astronomy
Durham University Universityof Manchester
Durham Manchester
UK UK
ISSN 2190-5053 ISSN 2190-5061 (electronic)
ISBN 978-3-319-01209-4 ISBN 978-3-319-01210-0 (eBook)
DOI 10.1007/978-3-319-01210-0
SpringerChamHeidelbergNewYorkDordrechtLondon
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(cid:2)SpringerInternationalPublishingSwitzerland2014
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Publications
The work in this thesis is partly based upon the following publications:
• Massive gravity, the elasticity of space-time, and perturbations in the dark
sector [259], with Richard Battye
• Effective action approach to cosmological perturbations in dark energy and
modified gravity [187], published in JCAP with Richard Battye.
• Effective field theory for perturbations in dark energy and modified gravity
[216], conference proceedings.
• Equations of state for dark sector perturbations for general high derivative
scalar-tensor theories: in preparation with Richard Battye.
• Parameterizing dark sector perturbations via equations of state: in preparation
with Richard Battye
• Observational signatures and constraints on generalized cosmological pertur-
bations: in preparation with Richard Battye and Adam Moss.
That there exist rules to be checked at all is
some sort of miracle
—Richard Feynman
Book-keeping, continued to all eternity,
could not produce one farthing
—C. S. Lewis
The creator does not appear in the scientific
account, but it is clearly ridiculous to deduce
from this that the creator did not exist
—John Lennox
In the beginning God created the heavens
and the earth. Now the earth was formless
and empty, darkness was over the surface of
the deep, and the Spirit of God was hovering
over the waters
—Genesis 1
To my parents, Marcus, and Anna
Supervisor’s Foreword
TheNobelPrizeforPhysicsin2011wasawardedjointlytoSaulPerlmutter,Adam
Reiss, and Brian Schmidt for the discovery of cosmic acceleration. However, its
origin is still one of the greatest mysteries in modern physics. A cosmological
constantis,perhaps,thesimplestexplanationbutitisdifficulttoreconcilewithour
understanding of modern particle physics theories that predicts a vacuum energy
120 orders of magnitude larger than observed. It has been suggested that a
dynamical component ofthe Universe, knownasdark energy,ormodificationsto
Einstein’s theory of General Relativity in the infrared could be responsible.
There are now many theories that have been proposed to describe dark energy
and modified gravity. Observations are likely to play a key role in distinguishing
thedifferenttheories.Therearetwoclassesofobservations:(i)thosethatareonly
sensitive to the background evolution; (ii) those that are, in addition, sensitive to
theevolutionofperturbations. Inparticular,weakgravitational lensingisaffected
bythedistributionofthedarkenergy,ortheevolutionofperturbationsinmodified
gravity. The observed distortions of galaxy shapes, or those observed in the
Cosmic Microwave Background, can be very different to those predicted for
models involving a cosmological constant.
The goal of this thesis was to develop a general formalism for modeling the
evolutionofperturbationsindarkenergyandmodifiedgravity.Thebasicideawas
to try to make as few theoretical assumptions as possible in deriving the obser-
vational predictions. The hope would then be that those analyzing observations
wouldmeasurethefreeparametersinthemodelandallowustohoneinthecorrect
theory.
Starting from the field content of a model and some basic arguments of sym-
metry, Jonathan was able to derive expressions for the effective fluid variables in
terms of the active degrees offreedom of whatever is causing the cosmic accel-
eration. In a number of cases, it was possible to eliminate the internal degrees of
freedomanddeduceanequationofstatefortheperturbationsthatisparameterized
xi
xii Supervisor’sForeword
byanumberoffreefunctionsoftime.Hethenwentontoperformasurveyofthe
possible observational consequences. In work done since the submission of the
thesis,wehaveextendedthebasicideatoawiderclassofmodelsand,atpresent,
we are investigating the constraints imposed from the recently released data from
the Planck satellite.
Manchester, June 2013 Prof. Richard Battye