Title: ASPECTS OF HORAVALIFSHITZ COSMOLOGY
1ASPECTS OF HORAVALIFSHITZ COSMOLOGY
Physics Department, University of Athens Greece
E.N.Saridakis HsinchuTaiwan, Nov 2010
2Goal
 We investigate cosmological scenarios in a
universe governed by HoravaLifshitz gravity
 Note
 A consistent or interesting cosmology is not a
proof for the consistency of the underlying
gravitational theory
E.N.Saridakis HsinchuTaiwan, Nov 2010
3Talk Plan
 1) Introduction HoravaLifshitz gravity and
cosmology  2) Phasespace analysis and latetime
cosmological behavior  3) Bouncing solutions and cyclic behavior
 4) Observational Constraints
 5) Thermodynamic aspects
 6) Perturbative instabilities
 7) ConclusionsProspects
E.N.Saridakis HsinchuTaiwan, Nov 2010
4Introduction
 HoravaLifshitz gravity powercounting
renormalizable, UV complete  IR fixed point General Relativity
 Good UV behavior Anisotropic, Lifshitz scaling
between time and space  Theoretical and conceptual problems
(instabilities etc)? Open subject.
Horava, PRD 79
E.N.Saridakis HsinchuTaiwan, Nov 2010
5Introduction HoravaLifshitz gravity
(detailedbalanced)
(extrinsic curvature) (Cotton tensor)
Kiritsis, Kofinas, NPB 821
E.N.Saridakis HsinchuTaiwan, Nov 2010
6 Introduction HoravaLifshitz cosmology
 Cosmological framework

(projectability) 
 Matter content

Kiritsis, Kofinas, NPB 821
E.N.Saridakis HsinchuTaiwan, Nov 2010
7 Introduction HoravaLifshitz cosmology
 Friedmann Equations (under detailed balance)


 and
Kiritsis, Kofinas, NPB 821
E.N.Saridakis HsinchuTaiwan, Nov 2010
8 Introduction HoravaLifshitz cosmology
 Friedmann Equations (under detailed balance)


 and
 Effective dark energy
Kiritsis, Kofinas, NPB 821
Leon, Saridakis, JCAP 0911
E.N.Saridakis HsinchuTaiwan, Nov 2010
9Introduction HoravaLifshitz cosmology
 Friedmann Equations (beyond detailed balance)


 Effective dark energy
Elizalde et al, CQG 27
Leon, Saridakis, JCAP 0911
E.N.Saridakis HsinchuTaiwan, Nov 2010
10Phasespace analysis
 Transform cosmological system to its autonomous
form 

 Linear Perturbations
 Eigenvalues of determine type and stability
of C.P
Leon, Saridakis, JCAP 0911
E.N.Saridakis HsinchuTaiwan, Nov 2010
11 Phasespace analysis
 Detailed balance
 P3 Stable with
P11 Saddle with
Leon, Saridakis, JCAP 0911
E.N.Saridakis HsinchuTaiwan, Nov 2010
12 Phasespace analysis
 Beyond Detailed Balance (4D problem)
 Stable solution with and
(eternally expanding)  Small probability (nonhyperbolid C.P) for an
Oscillating solution  (The terms responsible for the
bounce, and the c.c responsible for the
turnaround)
Leon, Saridakis, JCAP 0911
E.N.Saridakis HsinchuTaiwan, Nov 2010
13 Bounce and Cyclic behavior
 Contracting ( ), bounce ( ),
expanding ( )  near and at the bounce
 Expanding ( ), turnaround ( ),
contracting ( )  near and at the turnaround
E.N.Saridakis HsinchuTaiwan, Nov 2010
14 Bounce and Cyclic behavior
 Contracting ( ), bounce ( ),
expanding ( )  near and at the bounce
 Expanding ( ), turnaround ( ),
contracting ( )  near and at the turnaround
 Bounce and cyclicity can be easily obtained
Cai, Saridakis, JCAP 0910
Brandenberger, PRD 80
E.N.Saridakis HsinchuTaiwan, Nov 2010
15 Bounce and Cyclic behavior
 Input oscillatory

 Output
 Reconstructed
Cai, Saridakis, JCAP 0910
E.N.Saridakis HsinchuTaiwan, Nov 2010
16 Bounce and Cyclic behavior
Cai, Saridakis, JCAP 0910
Cai, Saridakis, JCAP 0910
E.N.Saridakis  Ischia, Sept 2009
E.N.Saridakis HsinchuTaiwan, Nov 2010
17Bounce and Cyclic behavior
 Input
 Output
 Important Processing of perturbations
Cai, Saridakis, JCAP 0910
Brandenberger, PRD 80,b
E.N.Saridakis HsinchuTaiwan, Nov 2010
18A more realistic dark energy
 In all the above discussion
 Observational indications that
today  Possible solution Insert a new scalar
(canonical) field  (see also f(R) HoravaLifshitz cosmology
)
 Quintessence, Phantom and Quintom Cosmology
 easily acquired
Saridakis, EJPC 65
Nojiri, Odintsov, CQG27
E.N.Saridakis HsinchuTaiwan, Nov 2010
19Observational constraints (detailedbalance)
 Use observational data (SNIa, BAO, CMB, BBN) to
constrain the parameters of the theory  Include matter and standard radiation
hydrodynamically

 Fix . Units
E.N.Saridakis HsinchuTaiwan, Nov 2010
20Observational constraints (detailedbalance)
 Use observational data (SNIa, BAO, CMB, BBN) to
constrain the parameters of the theory  Include matter and standard radiation
hydrodynamically

 Fix . Units
 4 dimensionless parameters to be fitted
 (we fix at its WAMP5 best fit value)
Dutta, Saridakis, JCAP 1001
E.N.Saridakis HsinchuTaiwan, Nov 2010
21Observational constraints (detailedbalance)
 At present
 Total radiation (standard plus dark) at
Nucleosynthesis  effective neutrino species.
 Thus, 4 dimensionless parameters to be fitted
 (we fix in terms of )

Olive,et al, Phys. Rept. 333
E.N.Saridakis HsinchuTaiwan, Nov 2010
22Observational constraints (detailedbalance)
 At present
 Total radiation (standard plus dark) at
Nucleosynthesis  effective neutrino species.
 Thus, 4 dimensionless parameters to be fitted
 (we fix in terms of )


 2 free parameters
Olive,et al, Phys. Rept. 333
Dutta, Saridakis, JCAP 1001
E.N.Saridakis HsinchuTaiwan, Nov 2010
23Observational constraints (detailedbalance)
(0, 0.0038) (0, 1.4189) (1.1872, )
(0.0039, 0) (0. 1.4063) (1.1925, )
Dutta, Saridakis, JCAP 1001
E.N.Saridakis HsinchuTaiwan, Nov 2010
24Observational constraints (beyond
detailedbalance)

 We fix at their WAMP5 best fit values
and is given in terms of them  So 4 dimensionless parameters to be fitted

(at present) 
(Nucleosynthesis) 
 2 free parameters for given
values of
Dutta, Saridakis, JCAP 1001
E.N.Saridakis HsinchuTaiwan, Nov 2010
25Observational constraints (beyond
detailedbalance)
0.1 (0, 0.01) (4.29, 4.33) (0, 0.03)
0.1 (0.01, 0) (4.40, 4.45) (0, 0.81)
2.0 (0, 0.04) (4.13, 4.45) (0, 0.01)
2.0 (0.01, 0) (4.40, 4.45) (0, 0.23)
Dutta, Saridakis, JCAP 1001
E.N.Saridakis HsinchuTaiwan, Nov 2010
26Observational constraints on ?
 Concerning cosmological observations is
expected to be very close to its IR value 1.  We perform an overall observational fitting,
allowing to vary along with the other
parameters of the theory.  Detailed balance
 Beyond detailed balance
 Repeat the aforementioned procedure.
Dutta, Saridakis, JCAP 1005
E.N.Saridakis HsinchuTaiwan, Nov 2010
27Observational constraints on ?
 Detailed balance
 Beyond detailed balance
Dutta, Saridakis, JCAP 1005
E.N.Saridakis HsinchuTaiwan, Nov 2010
28Thermodynamic Aspects
 Known connection between gravity and
thermodynamics.  Field Equations First Law of
Thermodynamics.  For a universe bounded by the apparent horizon
 one calculates the entropy of the universe
content, plus that of the horizon itself.
Furthermore, all the fluids inside the universe
have the same temperature with horizon.
E.N.Saridakis HsinchuTaiwan, Nov 2010
29Thermodynamic Aspects
 Known connection between gravity and
thermodynamics.  Field Equations First Law of
Thermodynamics.  For a universe bounded by the apparent horizon
 one calculates the entropy of the universe
content, plus that of the horizon itself.
Furthermore, all the fluids inside the universe
have the same temperature with horizon.  In an FRW universe in GR

R.G.Cai, Kim, JHEP 0502
E.N.Saridakis HsinchuTaiwan, Nov 2010
30Thermodynamic Aspects
 Known connection between gravity and
thermodynamics.  Field Equations First Law of
Thermodynamics.  For a universe bounded by the apparent horizon
 one calculates the entropy of the universe
content, plus that of the horizon itself.
Furthermore, all the fluids inside the universe
have the same temperature with horizon.  In an FRW universe in GR

 In the same lines for the Generalized Second Law
(GSL) of Thermodynamics  (entropy timevariation of the universe
content plus that of the horizon to be
nonnegative)
R.G.Cai, Kim, JHEP 0502
Bamba, Geng, Tsujikawa, PLB 688 0502
E.N.Saridakis HsinchuTaiwan, Nov 2010
31GSL in HoravaLifshitz cosmology (detailed
balance)
 The universe contains only matter. For its
entropy timevariation  with
.  with

 and
 So
E.N.Saridakis HsinchuTaiwan, Nov 2010
32GSL in HoravaLifshitz cosmology (detailed
balance)
 The universe contains only matter. For its
entropy timevariation  with
.  with

 and
 So
 The temperature of the universe content is equal
to that of the horizon  (depends only on
the universe geometry)  The entropy of the horizon equals that of a black
hole, with as a horizon
Jamil, Saridakis, Setare 1003.0876 hepth
R.G.Cai, Ohta PLB 679, PRD 81
E.N.Saridakis HsinchuTaiwan, Nov 2010
33GSL in HoravaLifshitz cosmology
 In total
 Clearly GSL is conditionally violated. Things are
worse beyond detail balance, where the correction
has not a standard sign.
Jamil, Saridakis, Setare 1003.0876 hepth
(to appear in JCAP)
E.N.Saridakis HsinchuTaiwan, Nov 2010
34 GSL in HoravaLifshitz cosmology
 In total
 Clearly GSL is conditionally violated. Things are
worse beyond detail balance, where the correction
has not a standard sign.  Should we take other horizon? Can we define
temperature, entropy or the horizon itself in HL
cosmology?  Or another sign against HL gravity?
 Interesting and Open Issues.
Jamil, Saridakis, Setare 1003.0876 hepth
(to appear in JCAP)
Kiritsis, Kofinas, JHEP 1001
E.N.Saridakis HsinchuTaiwan, Nov 2010
35Perturbative instabilities?
 So far we discussed about HL cosmology. A
consistent cosmology is not a proof for the
consistency of the underlying gravitational
theory. (It is necessary but not sufficient)  Is HL gravity robust?
E.N.Saridakis HsinchuTaiwan, Nov 2010
36 Perturbative instabilities?
 So far we discussed about HL cosmology. A
consistent cosmology is not a proof for the
consistency of the underlying gravitational
theory. (It is necessary but not sufficient)  Is HL gravity robust?
 Perturbations before analytic continuation

vector modes transverse (
) 
tensor mode transverse and traceless
( )  In synchronous gauge
 Degrees of freedom (scalar),
(vector), (tensor)
Bogdanos, Saridakis, CQG 27
E.N.Saridakis HsinchuTaiwan, Nov 2010
37Perturbative instabilities?
 Fourier transforming, the dispersion relation for
at low k 
at high k  For tensor mode we get
 Beyond detail balance (assume
) we
get  for scalar modes in the UV
 tensor modes
E.N.Saridakis HsinchuTaiwan, Nov 2010
38Perturbative instabilities?
 Fourier transforming, the dispersion relation for
at low k 
at high k  For tensor mode we get
 Beyond detail balance (assume
) we
get  for scalar modes in the UV
 tensor modes
 Cannot fix everything with analytic continuation
 (apart from the fact that this could
radically change the renormalizability properties
of the theory)  One could take ?0 but what about the light
speed?
Bogdanos, Saridakis, CQG 27
Charmousis, et al, JHEP 0908
E.N.Saridakis HsinchuTaiwan, Nov 2010
39Healthy extension of HoravaLifshitz gravity?
 So, one should search for extended versions of
HoravaLifshitz gravity  with
Kiritsis, PRD 81 R.G.Cai, Zhang
1008.5048
Blas, et al, PRL 104
E.N.Saridakis HsinchuTaiwan, Nov 2010
40Conclusions
 i) HoravaLifshitz gravity applied as a
cosmological framework  HoravaLifshitz cosmology. Very
interesting.  ii) Interesting latetime solution subclasses,
revealed by phasespace analysis. Amongst them an
eternally expanding DE dominated universe.  iii) We can obtain bouncing and cyclic behavior
 iv) We can use observations to constrain the
model parameters. ? is constrained in  v) The generalized second law of thermodynamics
is not valid  vi) However, there may be problems at
HoravaLifshitz gravity itself.  Perturbative instabilities, that cannot
be easily cured.  vii) Search for healthy extensions
E.N.Saridakis HsinchuTaiwan, Nov 2010
41Outlook
 Many cosmological subjects are open. Amongst
them  i) Calculate the ParametrizedPostNewtonian
(PPN) parameters for HL cosmology.  ii) Constrain observationally the minimal
extended version  iii) Examine the generalized second law in the
extended version  iv) And of course provide clues, arguments,
indications and proofs that HoravaLifshitz
gravity is indeed the underlying theory of
gravity.
E.N.Saridakis HsinchuTaiwan, Nov 2010
42E.N.Saridakis HsinchuTaiwan, Nov 2010