It is now an exceptional time for modern cosmology, when we can observe the universe with high precision and connect cosmological measurements with theory. The excitement about the advances of observational cosmology is accompanied by the awareness that we face some major challenges: we still lack compelling theoretical models for dark matter, (that accounts for the formation of the structure we see around us) , and dark energy, that drives cosmic acceleration, as well as a deeper understanding of the mechanism that set up primordial conditions, and these puzzles have deep roots in particle theory and gravity.I will focus on the challenge posed by dark energy and discuss theoretical issues involved in finding an optimal framework to unveil its nature from upcoming high precision measurements of large scale structure, giving an overview of recent progress.

1. Alessandra Silvestri
Instituut Lorentz, Leiden U.
Lighting up Einstein’s Dark Universe
Nordwijk, November 30 2018ESTEC

2. Einstein 1915
Cosmology

3. Einstein 1915
Hubble 1929
First experimental confirmation came shortly
after, when Hubble measured the velocity of
distant galaxies:
Cosmology

4. Successes of Observational Cosmology

5. CMB
Bullet Cluster
Galaxy rotation curves
Lensing
Large Scale Structure
Type Ia Supernovae
BBN Nucleosynthesis
Successes of Observational Cosmology

6. CMB
Bullet Cluster
Galaxy rotation curves
Lensing
Large Scale Structure
Type Ia Supernovae
BBN Nucleosynthesis
Successes of Observational Cosmology
The universe expands.
It is spatially flat and
homogeneous & isotropic on the large scales.
It has been expanding since the Big
Bang, ....., there was a radiation dominated
era, then a matter era when structure
formed,....
It contains visible matter with a fractional
energy density of ~ 0.05 (today).
...

7. CMB
Bullet Cluster
Galaxy rotation curves
Lensing
Large Scale Structure
Type Ia Supernovae
BBN Nucleosynthesis
Successes of Observational Cosmology
The universe expands.
It is spatially flat and
homogeneous & isotropic on the large scales.
It has been expanding since the Big
Bang, ....., there was a radiation dominated
era, then a matter era when structure
formed,....
It contains visible matter with a fractional
energy density of ~ 0.05 (today).
...
STANDARD MODEL OF COSMOLOGY:
LCDM

8. We still lack theoretically compelling models for what is
making up ~95% of the current energy budget of the universe
DARK
MATTER
… and a quite dark Universe !

9. We still lack theoretically compelling models for what is
making up ~95% of the current energy budget of the universe
… and a quite dark Universe !

10. We still lack theoretically compelling models for what is
making up ~95% of the current energy budget of the universe
Stockholm, Dec. 2011
… and a quite dark Universe !

11. source of
acceleration?

12. Λdynamical
DE
modified
gravity
backreaction
EinsteinwegLeVerrierweg source of
acceleration?

13. massless spin-2
graviton
massive spin-2
graviton
minimally
coupled
non-minimally
coupled
landscape
broken
Lorentz-inv.
Λdynamical
DE
modified
gravity
backreaction
EinsteinwegLeVerrierweg source of
acceleration?

14. massless spin-2
graviton
massive spin-2
graviton
minimally
coupled
non-minimally
coupled
landscape
broken
Lorentz-inv.
f(R)
IR
modifications
scalar-tensor
theories
quintessence
k-essence
ghost
condensate
degravitation
Infinite
extra-dimensions
DGP
bi-metric
theories
TeVeS
Galileons
KK
Λdynamical
DE
modified
gravity
backreaction
EinsteinwegLeVerrierweg source of
acceleration?

15. discrepancies in Uranus’s
observed orbit
discovery of Neptune
(1846)
Le Verrier
We’ve been there already!

16. discrepancies in Uranus’s
observed orbit
discovery of Neptune
(1846)
Le Verrier
precession of Mercury’s
orbit
General Relativity
(1915)
Einstein
We’ve been there already!

17. discrepancies in Uranus’s
observed orbit
discovery of Neptune
(1846)
(DARK ENERGY)
(MODIFIED GRAVITY)
Le Verrier
precession of Mercury’s
orbit
General Relativity
(1915)
Einstein
We’ve been there already!

18. Ongoing and upcoming wide field imaging and
spectroscopic redshift surveys are in line to
map more than a 100 cubic-billion-light-year
of the Universe providing exquisite
measurements of expansion rate &
distribution of matter to ~ O(1)% over wide
redshift range.
eBOSS
Observational Cosmology comes to the rescue!
ELT

19. baryons
neutrinos
photons
dark mattergµ⌫
dark energy
Cosmic drama
Gµ⌫ =
Tµ⌫
M2
P
geometry matter

20. expansion history:
flat FLRW metric
a(⌧)
ds2
= a2
(⌧)
⇥
d⌧2
d~x2
⇤
Hubble parameter
Background
H ⌘
dlna
d⌧
=
a2
3M2
P
⇢

21. expansion history:
flat FLRW metric
a(⌧)
ds2
= a2
(⌧)
⇥
d⌧2
d~x2
⇤
Hubble parameter
Background
H ⌘
dlna
d⌧
=
a2
3M2
P
⇢
only if GR
is the correct
theory of gravity

22. : non-relativistic tracers
orbits of planets
galaxies: growth of structure
and
peculiar velocities
Newtonian potential
Large Scale Structure

23. : non-relativistic tracers
orbits of planets
galaxies: growth of structure
and
peculiar velocities
Newtonian potential
Large Scale Structure

24. : massless particles
weak lensing,
Integrated Sachs-Wolfe effect in CMB
light deflection, time delay
lensing potential
Eddington, 1919
Large Scale Structure
+

25. / ⇢ + / ⇢

26. / ⇢ + / ⇢
if GR is the correct theory of gravity:
=
+
2
=
a2
2M2
P k2
⇢
Poisson eq.

27. Together, dark matter and dark energy
pose some of the most important
questions in fundamental physics today.
....
Euclid is a high-precision survey mission
optimised for two independent
cosmological probes:
1.Weak Gravitational Lensing.
from a high-resolution imaging survey
.....
2. Galaxy Clustering
measured via a massive spectroscopic
redshift survey
...
coming soon !
EUCLID

28. 20 Mpc/h
D U S T G R A I N
⇤ C D M z = 0
courtesy of Marco Baldi

29. 20 Mpc/h
D U S T G R A I N
f R 4 z = 0
courtesy of Marco Baldi

30. Casas et al., Phys. Dark Univ. 2017
WL
GC
GC+WL+Planck
EUCLID
deviations
in WL
deviations
in GC

31. Casas et al., Phys. Dark Univ. 2017
WL
GC
GC+WL+Planck
EUCLID
1-10% on µ ⌃
1% on w(a)
,
deviations
in WL
deviations
in GC

32. We will have wonderful
numbers.
Will we be able to extract
the (correct) physics out of
them?

33. Declaring ignorance …
… but in an informed way !

34. Gubitosi, Piazza,Vernizzi, JCAP 1302 (2013) 032 Piazza,Vernizzi, Class.Quant.Grav. 30 (2013) 214007 Bloomfield, Flanagan, Park,Watson JCAP 1308 (2013) 010
S =
Z
d4
x
p
g
⇢
m2
0
2
[1 + ⌦(⌧)] R + ⇤(⌧) a2
c(⌧) g00
+
M4
2 (⌧)
2
(a2
g00
)2
¯M3
1 (⌧)
2
a2
g00
Kµ
µ
¯M2
2 (⌧)
2
( Kµ
µ )2
¯M2
3 (⌧)
2
Kµ
⌫ K⌫
µ +
a2 ˆM2
(⌧)
2
g00
R(3)
+ . . . + Sm[gµ⌫]
IN UNITARY GAUGE
Frusciante, Papadomanolakis,AS, JCAP 1607 (2016)J. Gleyzes et al., Phys.Rev.Lett. 114 (2015) R. Kase, S.Tsujikawa, Int.J.Mod.Ph
Declaring ignorance …
… but in an informed way !

35. Gubitosi, Piazza,Vernizzi, JCAP 1302 (2013) 032 Piazza,Vernizzi, Class.Quant.Grav. 30 (2013) 214007 Bloomfield, Flanagan, Park,Watson JCAP 1308 (2013) 010
S =
Z
d4
x
p
g
⇢
m2
0
2
[1 + ⌦(⌧)] R + ⇤(⌧) a2
c(⌧) g00
+
M4
2 (⌧)
2
(a2
g00
)2
¯M3
1 (⌧)
2
a2
g00
Kµ
µ
¯M2
2 (⌧)
2
( Kµ
µ )2
¯M2
3 (⌧)
2
Kµ
⌫ K⌫
µ +
a2 ˆM2
(⌧)
2
g00
R(3)
+ . . . + Sm[gµ⌫]
IN UNITARY GAUGE
Frusciante, Papadomanolakis,AS, JCAP 1607 (2016)J. Gleyzes et al., Phys.Rev.Lett. 114 (2015) R. Kase, S.Tsujikawa, Int.J.Mod.Ph
Declaring ignorance …
… but in an informed way !

36. Gubitosi, Piazza,Vernizzi, JCAP 1302 (2013) 032 Piazza,Vernizzi, Class.Quant.Grav. 30 (2013) 214007 Bloomfield, Flanagan, Park,Watson JCAP 1308 (2013) 010
S =
Z
d4
x
p
g
⇢
m2
0
2
[1 + ⌦(⌧)] R + ⇤(⌧) a2
c(⌧) g00
+
M4
2 (⌧)
2
(a2
g00
)2
¯M3
1 (⌧)
2
a2
g00
Kµ
µ
¯M2
2 (⌧)
2
( Kµ
µ )2
¯M2
3 (⌧)
2
Kµ
⌫ K⌫
µ +
a2 ˆM2
(⌧)
2
g00
R(3)
+ . . . + Sm[gµ⌫]
IN UNITARY GAUGE
Frusciante, Papadomanolakis,AS, JCAP 1607 (2016)J. Gleyzes et al., Phys.Rev.Lett. 114 (2015) R. Kase, S.Tsujikawa, Int.J.Mod.Ph
Declaring ignorance …
… but in an informed way !

37. Gubitosi, Piazza,Vernizzi, JCAP 1302 (2013) 032 Piazza,Vernizzi, Class.Quant.Grav. 30 (2013) 214007 Bloomfield, Flanagan, Park,Watson JCAP 1308 (2013) 010
S =
Z
d4
x
p
g
⇢
m2
0
2
[1 + ⌦(⌧)] R + ⇤(⌧) a2
c(⌧) g00
+
M4
2 (⌧)
2
(a2
g00
)2
¯M3
1 (⌧)
2
a2
g00
Kµ
µ
¯M2
2 (⌧)
2
( Kµ
µ )2
¯M2
3 (⌧)
2
Kµ
⌫ K⌫
µ +
a2 ˆM2
(⌧)
2
g00
R(3)
+ . . . + Sm[gµ⌫]
IN UNITARY GAUGE
Frusciante, Papadomanolakis,AS, JCAP 1607 (2016)J. Gleyzes et al., Phys.Rev.Lett. 114 (2015) R. Kase, S.Tsujikawa, Int.J.Mod.Ph
Declaring ignorance …
… but in an informed way !

38. Gubitosi, Piazza,Vernizzi, JCAP 1302 (2013) 032 Piazza,Vernizzi, Class.Quant.Grav. 30 (2013) 214007 Bloomfield, Flanagan, Park,Watson JCAP 1308 (2013) 010
S =
Z
d4
x
p
g
⇢
m2
0
2
[1 + ⌦(⌧)] R + ⇤(⌧) a2
c(⌧) g00
+
M4
2 (⌧)
2
(a2
g00
)2
¯M3
1 (⌧)
2
a2
g00
Kµ
µ
¯M2
2 (⌧)
2
( Kµ
µ )2
¯M2
3 (⌧)
2
Kµ
⌫ K⌫
µ +
a2 ˆM2
(⌧)
2
g00
R(3)
+ . . . + Sm[gµ⌫]
IN UNITARY GAUGE
Frusciante, Papadomanolakis,AS, JCAP 1607 (2016)J. Gleyzes et al., Phys.Rev.Lett. 114 (2015) R. Kase, S.Tsujikawa, Int.J.Mod.Ph
Declaring ignorance …
… but in an informed way !

39. Gubitosi, Piazza,Vernizzi, JCAP 1302 (2013) 032 Piazza,Vernizzi, Class.Quant.Grav. 30 (2013) 214007 Bloomfield, Flanagan, Park,Watson JCAP 1308 (2013) 010
S =
Z
d4
x
p
g
⇢
m2
0
2
[1 + ⌦(⌧)] R + ⇤(⌧) a2
c(⌧) g00
+
M4
2 (⌧)
2
(a2
g00
)2
¯M3
1 (⌧)
2
a2
g00
Kµ
µ
¯M2
2 (⌧)
2
( Kµ
µ )2
¯M2
3 (⌧)
2
Kµ
⌫ K⌫
µ +
a2 ˆM2
(⌧)
2
g00
R(3)
+ . . . + Sm[gµ⌫]
IN UNITARY GAUGE
Frusciante, Papadomanolakis,AS, JCAP 1607 (2016)J. Gleyzes et al., Phys.Rev.Lett. 114 (2015) R. Kase, S.Tsujikawa, Int.J.Mod.Ph
Declaring ignorance …
… but in an informed way !

40. S
(2)
⇠,hT =
1
(2⇡)3
Z
d3
k dt a3
⇢h
L ˙⇠ ˙⇠
˙⇠2
k2
G⇠2
i
+
AT
8
⇣
˙hT
ij
⌘2 c2
T
a2
hT
ij
2
Theoretical priors
Frusciante, Papadomanolakis,AS, JCAP 1607 (2016).

41. S
(2)
⇠,hT =
1
(2⇡)3
Z
d3
k dt a3
⇢h
L ˙⇠ ˙⇠
˙⇠2
k2
G⇠2
i
+
AT
8
⇣
˙hT
ij
⌘2 c2
T
a2
hT
ij
2
Theoretical priors
Frusciante, Papadomanolakis,AS, JCAP 1607 (2016).

42. S
(2)
⇠,hT =
1
(2⇡)3
Z
d3
k dt a3
⇢h
L ˙⇠ ˙⇠
˙⇠2
k2
G⇠2
i
+
AT
8
⇣
˙hT
ij
⌘2 c2
T
a2
hT
ij
2
Theoretical priors
Frusciante, Papadomanolakis,AS, JCAP 1607 (2016).
Expanding the given action up to second order in the perturbations, and removing spurious DOFs,
we can inspect the dynamics of perturbations; in this case one scalar field, i.e. ξ, and the tensor:
L ˙⇠ ˙⇠ > 0
c2
s ⌘
G
L ˙⇠ ˙⇠
> 0
AT > 0
c2
T > 0
S
(2)
⇠,hT =
1
(2⇡)3
Z
d3
k dt a3
⇢h
L ˙⇠ ˙⇠
˙⇠2
k2
G⇠2
i
+
AT
8
⇣
˙hT
ij
⌘2 c2
T
a2
hT
ij
2

43. S
(2)
⇠,hT =
1
(2⇡)3
Z
d3
k dt a3
⇢h
L ˙⇠ ˙⇠
˙⇠2
k2
G⇠2
i
+
AT
8
⇣
˙hT
ij
⌘2 c2
T
a2
hT
ij
2
Theoretical priors
Frusciante, Papadomanolakis,AS, JCAP 1607 (2016).
Expanding the given action up to second order in the perturbations, and removing spurious DOFs,
we can inspect the dynamics of perturbations; in this case one scalar field, i.e. ξ, and the tensor:
L ˙⇠ ˙⇠ > 0
c2
s ⌘
G
L ˙⇠ ˙⇠
> 0
AT > 0
c2
T > 0
S
(2)
⇠,hT =
1
(2⇡)3
Z
d3
k dt a3
⇢h
L ˙⇠ ˙⇠
˙⇠2
k2
G⇠2
i
+
AT
8
⇣
˙hT
ij
⌘2 c2
T
a2
hT
ij
2

44. Peirone, Raveri, Pogosian,AS, Koyama, PRD 2018
(µ,Σ) in Horndeski
deviations
in WL
deviations
inGC

45. Peirone, Raveri, Pogosian,AS, Koyama, PRD 2018
(µ,Σ) in Horndeski
deviations
in WL
deviations
inGC
(Most) general theory of gravity which
propagates the usual massless tensor
(graviton) and an additional scalar
degree of freedom, with second order
equations of motion.
by G. Horndeski
Talking about gravity

46. Peirone, Raveri, Pogosian,AS, Koyama, PRD 2018
(µ,Σ) in Horndeski
deviations
in WL
deviations
inGC
(Most) general theory of gravity which
propagates the usual massless tensor
(graviton) and an additional scalar
degree of freedom, with second order
equations of motion.
by G. Horndeski
Talking about gravity

47. Gravitational Waves
‘After straining our eyes, it is now time to strain our ears !’OCTOBER 2017

48. ¨hij + 2H˙hij + c2
T k2
hij = 0
Ripples in the fabric of spacetime described by the tensor .
3 · 10 15
<
c2
T
c2
1 < 7 · 10 16
GW170817
& GRB170817A
, they placed very stringent limits on the speed of gravity:
Using the observed time-delay btw GRB and GW,
In a cosmological background they propagate according to:
(1.74 ± 0.05) s
hij
c2
T = 1

49. Peirone, Raveri, Pogosian,AS, Koyama, PRD 2018
(µ,Σ) in Horndeski + GWs bound
time
scale
c2
T = 1

50. Peirone, Raveri, Pogosian,AS, Koyama, PRD 2018
(µ,Σ) in Horndeski + GWs bound
time
scale
c2
T = 1

51. No gravitational slip on large scales!(k ⌧ Ma) = (k ⌧ Ma)
Pogosian & Silvestri PRD 2016
Synergy!
clustering = lensing
µ = ⌃c2
T = 1 for Horndeski
on large scales

52. No gravitational slip on large scales!(k ⌧ Ma) = (k ⌧ Ma)
Euclid will measure this with ~1-10% accuracy.
Were we to find a non-null value, then we would detect
some beyond Horndeski.
Pogosian & Silvestri PRD 2016
Synergy!
clustering = lensing
µ = ⌃c2
T = 1 for Horndeski
on large scales

53. How does gravity look like on
cosmological scales?
What is sourcing the accelerated
expansion of the Universe?
What can Large Scale Structure tell us
about fundamental physics?
The questions that we pursue

54. Wrapping up!
We are making progress in terms of theoretical frameworks to interpret
upcoming data ... bare with us, next years will be exciting!

55. Redshift
For objects at small distances:
z ⇡ v = H0d
Everything we know in the Universe, (so far) is inferred from the light we
receive from distant objects.
As the Universe expands, the light from distant sources is stretched out so that the
observed wavelength is larger than the emitted one.
We define the REDSHIFT as this stretching factor:
z + 1 ⌘
obs
emit

56. Redshift
The bigger the z, the bigger the distance, but by how much precisely?
?
But on cosmological scales, things are more complicated, as light travels space expands at a rate
that changes with time…
z $ d

57. Redshift
The bigger the z, the bigger the distance, but by how much precisely?
?
But on cosmological scales, things are more complicated, as light travels space expands at a rate
that changes with time…
H(z)
z $ d

58. Redshift
The bigger the z, the bigger the distance, but by how much precisely?
?
But on cosmological scales, things are more complicated, as light travels space expands at a rate
that changes with time…
H(z)
z $ d
PHYSICS
GRAVITY
MATTER

59. ds2
= N2
dt2
+ hij(dxi
+ Ni
dt)(dxj
+ Nj
dt)
lapse function shift vector
3D metric
hµ⌫ = gµ⌫ + nµn⌫nµ ⌘ Nt;µ
Kµ⌫ = hµn⌫;µ
R(3)
µ⌫intrinsic curvature:
extrinsic curvature: Kij =
1
2N
(@thij riNj rjNi)
If we define:
A unified action
The presence of an extra dynamical scalar d.o.f. wrt the standard model of cosmology naturally
singles out a preferred foliation of space-time.
It is natural to employ the ADM (Arnowitt-Deser-Misner) decomposition of spacetime:

60. ds2
= N2
dt2
+ hij(dxi
+ Ni
dt)(dxj
+ Nj
dt)
lapse function shift vector
3D metric
hµ⌫ = gµ⌫ + nµn⌫nµ ⌘ Nt;µ
Kµ⌫ = hµn⌫;µ
R(3)
µ⌫intrinsic curvature:
extrinsic curvature: Kij =
1
2N
(@thij riNj rjNi)
If we define:
A unified action
The presence of an extra dynamical scalar d.o.f. wrt the standard model of cosmology naturally
singles out a preferred foliation of space-time.
nµ ⌘
@µ
p
(@µ )2UNITARY GAUGE
And the action is built out of all geometrical quantities that are invariant under the time-dependent
3D spatial diffeomorphisms.
It is natural to employ the ADM (Arnowitt-Deser-Misner) decomposition of spacetime:

61. GW170817
& GRB170817A
LIGO,Virgo, Fermi,-GBM, INTEGRAL,Astrophys.J. 848 (2017)

62. The electromagnetic counterpart
allows us to determine the redshift
of the source.
GW170817
& GRB170817A
LIGO,Virgo, Fermi,-GBM, INTEGRAL,Astrophys.J. 848 (2017)

63. The aftermath of GW170817
& GRB170817A
¨hij +
2H(1 + ⌦) + ˙⌦
m2
0(1 + ⌦) ¯M2
3
m2
0
˙hij +

1 +
¯M2
3
(1 + ⌦) ¯M2
3
hij = 0
Horndeski gravity, in the EFT language gives:
c2
T = 1

64. The aftermath of GW170817
& GRB170817A
¨hij +
2H(1 + ⌦) + ˙⌦
m2
0(1 + ⌦) ¯M2
3
m2
0
˙hij +

1 +
¯M2
3
(1 + ⌦) ¯M2
3
hij = 0
Horndeski gravity, in the EFT language gives:
conformal coupling
non-trivial kinetic term
c2
T = 1

65. The aftermath of GW170817
& GRB170817A
¨hij +
2H(1 + ⌦) + ˙⌦
m2
0(1 + ⌦) ¯M2
3
m2
0
˙hij +

1 +
¯M2
3
(1 + ⌦) ¯M2
3
hij = 0
Horndeski gravity, in the EFT language gives:
conformal coupling
non-trivial kinetic term
Covariant Galileons, as well as quartic and quintic Horndeski, are gone.
This cuts a big chunk of self-accelerating models.
Creminelli &Vernizzi, PRL 2017
Ezquiaga, Zumalacarregui, PRL 2017
Baker et al., PRL 2017
c2
T = 1

66. What goes on @ LION
Cosmology group
A. Achucarro
A. Boyarsky
A. Silvestri
K. Schalm