Scalar-field dark energy models: Current and forecast constraints

Abstract

Recent results from type Ia supernovae (SNe Ia) and baryon acoustic oscillations (BAO), in combination with cosmic microwave background (CMB) measurements, have focused renewed attention on dark energy models with a time-varying equation-of-state parameter, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>w</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>z</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> . In this paper, we describe the simplest, physically motivated models of evolving dark energy that are consistent with the recent data, a broad subclass of the so-called thawing scalar-field models that we dub <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>w</e:mi> <e:mi>ϕ</e:mi> </e:msub> <e:mi>CDM</e:mi> </e:math> . We provide a quasiuniversal, quasi-one-parameter functional fit to the scalar-field <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>w</g:mi> <g:mi>ϕ</g:mi> </g:msub> <g:mo stretchy="false">(</g:mo> <g:mi>z</g:mi> <g:mo stretchy="false">)</g:mo> </g:math> that captures the behavior of these models more informatively than the standard <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>w</k:mi> <k:mn>0</k:mn> </k:msub> <k:msub> <k:mi>w</k:mi> <k:mi>a</k:mi> </k:msub> </k:math> phenomenological parametrization; their behavior is completely described by the current value of the equation-of-state parameter, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>w</m:mi> <m:mn>0</m:mn> </m:msub> <m:mo>=</m:mo> <m:mi>w</m:mi> <m:mo stretchy="false">(</m:mo> <m:mi>z</m:mi> <m:mo>=</m:mo> <m:mn>0</m:mn> <m:mo stretchy="false">)</m:mo> </m:math> . Combining current data from BAO (DESI data release 2), the CMB ( and ACT), large-scale structure (DES year-3 <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mn>3</q:mn> <q:mo>×</q:mo> <q:mn>2</q:mn> <q:mi>pt</q:mi> </q:math> ), SNe Ia (DES-SN5YR), and strong lensing ( <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mrow> <s:mi>TDCOSMO</s:mi> <s:mo>+</s:mo> <s:mi>SLACS</s:mi> </s:mrow> </s:math> ), for <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi>w</u:mi> <u:mi>ϕ</u:mi> </u:msub> <u:mi>CDM</u:mi> </u:math> , we obtain <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msub> <w:mi>w</w:mi> <w:mn>0</w:mn> </w:msub> <w:mo>=</w:mo> <w:mo>−</w:mo> <w:mn>0.90</w:mn> <w:msubsup> <w:mn>4</w:mn> <w:mrow> <w:mo>−</w:mo> <w:mn>0.033</w:mn> </w:mrow> <w:mrow> <w:mo>+</w:mo> <w:mn>0.034</w:mn> </w:mrow> </w:msubsup> </w:math> , <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mrow> <y:mn>2.9</y:mn> <y:mi>σ</y:mi> </y:mrow> </y:math> discrepant from the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi mathvariant="normal">Λ</ab:mi> </ab:math> cold dark matter ( <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:mi mathvariant="normal">Λ</db:mi> <db:mi>CDM</db:mi> </db:math> ) model. The Bayesian evidence ratio substantially favors this <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:msub> <gb:mi>w</gb:mi> <gb:mi>ϕ</gb:mi> </gb:msub> <gb:mi>CDM</gb:mi> </gb:math> model over <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi mathvariant="normal">Λ</ib:mi> <ib:mi>CDM</ib:mi> </ib:math> . The data combination that yields the strongest discrepancy with <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:mi mathvariant="normal">Λ</lb:mi> <lb:mi>CDM</lb:mi> </lb:math> is <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:mrow> <ob:mi>BAO</ob:mi> <ob:mo>+</ob:mo> <ob:mi>SNe</ob:mi> </ob:mrow> </ob:math> Ia, for which <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:msub> <qb:mi>w</qb:mi> <qb:mn>0</qb:mn> </qb:msub> <qb:mo>=</qb:mo> <qb:mo>−</qb:mo> <qb:mn>0.83</qb:mn> <qb:msubsup> <qb:mn>7</qb:mn> <qb:mrow> <qb:mo>−</qb:mo> <qb:mn>0.045</qb:mn> </qb:mrow> <qb:mrow> <qb:mo>+</qb:mo> <qb:mn>0.044</qb:mn> </qb:mrow> </qb:msubsup> </qb:math> , <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"> <sb:mn>3.6</sb:mn> <sb:mi>σ</sb:mi> </sb:math> discrepant from <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"> <ub:mi mathvariant="normal">Λ</ub:mi> <ub:mi>CDM</ub:mi> </ub:math> and with a Bayesian evidence ratio strongly in favor. We find that the so-called <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"> <xb:msub> <xb:mi>S</xb:mi> <xb:mn>8</xb:mn> </xb:msub> </xb:math> tension between the CMB and large-scale structure is slightly reduced in these models, while the Hubble tension is slightly increased. We forecast constraints on these models from near-future surveys (DESI-extension and the Vera C. Rubin Observatory LSST), showing that the current best-fit <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"> <zb:msub> <zb:mi>w</zb:mi> <zb:mi>ϕ</zb:mi> </zb:msub> <zb:mi>CDM</zb:mi> </zb:math> model will be distinguishable from <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"> <bc:mi mathvariant="normal">Λ</bc:mi> <bc:mi>CDM</bc:mi> </bc:math> at over <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"> <ec:mrow> <ec:mn>9</ec:mn> <ec:mi>σ</ec:mi> </ec:mrow> </ec:math> .

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