ISCO2023, OIST
27 Feb. 2023

InflationandGravitational Wave Cosmology
Misao Sasaki
Kavli IPMU, University of Tokyo

Inflation2

What is Inflation?
Brout, Englert & Gunzig ’77, Starobinsky ’79, Guth ’81, Sato ’81, Linde ’81,…

Ø Inflation is a quasi-exponential expansion of the Universe
at its very early stage; perhaps at t~10-34 sec.
Ø It was meant to solve the initial condition (singularity,horizon & flatness, etc.) problems in Big-Bang Cosmology:
if any of them can be said to be solved depends on
precise definitions of the problems.

Ø Quantum vacuum fluctuations during inflation turn out toplay the most important role. They give the initial condition
for all the structures in the Universe.
Ø Cosmic gravitational wave background is also generated.
3

Inflation in a nutshell• Inflation is driven by a potential energy V(f ) of a scalar field f• f evolves very slowly: V≈ const.
expansion induces effective friction
friction-dominated, over-damped

V(f)energy density r remains
almost constant in time•

fFriedmann eq. (time-time component of Einstein eq.)

3𝐻 ! = 8𝜋𝐺𝜌: expansion rate of the Universe
cosmic scale factor•

Volume ∝ 𝑎3

if r =const. , H =const.

Volume expands exponentially = Inflation!
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Quantum fluctuations in Inflationary Universe
vacuum fluctuations due to uncertainty principle Δ𝑝Δ𝑥 = ℏℏ=7x10-16 eV# sthey exist only on micro scales; never appear on macro scales

But,exponential expansion stretches
vacuum fluctuations to macroscopic
scales and fluctuations become frozen

Δ𝑥 → ∞, ∆𝑝 → 0

origin of all the structures(stars, life, etc.)
in the Universe5Cosmological thermal history
reachable by GW obs
reachable by EMW obs

thermal equilibrium
end of inflation

end of hot universe
6Planck Cosmic Microwave Background Map
Planck 2015/2018
Sachs-Wolfe effectgravitational
redshiftbut contains important info!

Doppler effectprimordial vacuum fluctuations
produce Y and v(and induce fluctuations in matter)
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Planck CMB anisotropy spectrum
https://www.cosmos.esa.int/web/planck/picture-gallery

TT spectrum

theory(best fit model)

TE correlation

E: E-mode polarization

https://arxiv.org/abs/0811.3919observational data perfectly agree with inflationary predictions
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Inflation as GW source

9length scales of the inflationary universe
targets for multi-frequency GW cosmology
log L

L=H0-11028cm

Size of the Observable Universe
Hubble horizon(size of causal region)

L(t)
a
∝

k=108cm

CMBPTA
LISA

LIGO/Virgot.
snco(102~106(?)cm)

log a(t)Inflationary Universe

Hot Bigbang Universe
10Current and future GW detectors
CMB B-mode: SP4, LiteBIRD…

Pulsar Timing Array (PTA)

https://www.ipmu.jp/en/researchactivities/research-program/LiteBIRD

credit: David Champion

Space-based IFO’s: LISA, Taiji …

Ground-based IFO’s:
LIGO/Virgo/KAGRA …

https://www.ligo.caltech.edu/
credit: ESA

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GWs: New window to explore the Unknown Universe!
hPulsar Timing Array

Spaced-based
Ground-basedf
http://gwplotter.com/
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GWs from InflationØ scalar field(s) produce density fluctuations-> CMB temp + E-modeØ tensor (GW) fluctuations-> CMB temp + E-mode + B-mode
fluct ’nserutareptem

E-mode (even parity)

B-mode (odd parity)= cannot be produced
from density fluctuations

http://www.skyandtelescope.com/ization
rlaopedB-mo

Harvard-Smithsonian Center for Astrophysics

CMB B-mode = cosmological GW detector!
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GW spectrum from vanilla inflation
Can GWs from inflation be detected?
: strain amplitude

maybe just below sensitivity…

vanilla inflationary prediction
Renzini et al. 2202.00178
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Blue-tilted GW spectrum?
possible e.g. in massive gravity inflation model Lin & MS (2015): tensor mass during inflation = fcn of inflaton
spectral index:

WGWf [Hz]Ø many other models that produce detectable GWs existe.g., review by Caprini & Figueroa 201815

Primordial Black Holes
andinduced GWs

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PBH formation in a nutshell•

PBHs are those formed in the very
early universe, conventionally when
the universe was radiationdominated. Hawking ‘71, Carr & Hawking ‘74•

Presumably they originate from alarge positive curvature perturbation
produced during inflation (which
hence should be a rare event).

•

comoving length (∝ 𝑎)

O(1)For a BH to form, the perturbation
amplitude must be O(1) on theHubble horizon scale.

𝑴𝐏𝐁𝐇~ 𝑴𝐡𝐨𝐫𝐢𝐳𝐨𝐧~"##$%& !
ℓ𝑀⊙~ "*+'PBH!

𝑀⊙timeHubble radius = H-1 (∝ 𝑎! )17

iGWs can capture PBHs!

pegr
la

BHsPformskea

PBHs probe tail of prob distribution

curvature
perturbation
NL e
ffec
tindu

PBH

ce s

GWs

PBHs = CDM with MPBH ~1021g
generates GWs with f~10-3 Hz

spacetime oscillations
iGWs probe power spectrum

GWs in LISA band

CDM=Cold Dark Matter

PBHs = LV BHs with MPBH ~10M⊙
generates GWs with f~10-8 Hz
LV=LIGO-Virgo

GWs in PTA band
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GWs can test PBH scenario!
PBHs = LV BHs?

PBHs = CDM?

(Ω!"# ℎ$ , 𝑀!"# ) = (10%& , 100𝑀⊙ )(Ω!"# ℎ$ , 𝑀!"# ) = (10%( ,10$) g)

Saito & Yokoyama 0812.4339

Ø PBHs = LV BHs scenario is already constrained by NANOGrav (PTA)
Cai, Pi, Wang & Yang 1907.06372
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iGWs in non-minimal curvaton model
Pi & MS, 2112.12680

fractionin CDM

PBH mass function

The model predicts a highly
non-Gaussian tail in PDF forthe curvature perturbationiGW spectrum
inTi
anQ

ijiTa

𝑟=1𝑟 = 10%*LISA

peak:

PBH=CDM scenario can be clearly
verified or falsified by LISA!

r <<1 = stronger non-Gaussianity

20Summary* Inflation has become the standard model of the Universe* Cosmological GWs are the key to confirmation of inflation* Era of multi-band GW cosmology has begun!
CDM may be PBHs!
future GW detectors will prove/disprove the scenario.
* Entire stage of inflation may be probed by GWs* Astrophysical GWs also play essential roles

GWs will be an essential tool to explore
the Physics of the Unknown Universe!
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Stay tuned!
Thank you!
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