Probing gravity theory and cosmic acceleration using (in)consistency tests between cosmological data sets

Transcription

1 Probing gravity theory and cosmic acceleration using (in)consistency tests between cosmological data sets Prof. Mustapha Ishak Cosmology and Astrophysics Group The University of Texas at Dallas work done with my student Weikang Lin Lin & Ishak, Phys. Rev. D 96, (2017) arxiv: Lin & Ishak, Phys. Rev. D 96, (2017) arxiv: Mustapha Ishak, AAS Denver

2 At least two reasons to test the validity of gravity theory at cosmological scales (1) Finding out if cosmic acceleration is due to Dark Energy or Modified Gravity? (2) Is Einstein s theory of gravity modified or extended at cosmological scales? 2 Mustapha Ishak, AAS Denver 2018 Do you mean that I made a mistake? Albert Einstein

3 Inconsistencies between cosmological data sets constitute new revealing tools Our standard model of cosmology has parameters that encode our understanding and knowledge of the universe (e.g. age, rate of expansion ) Different data sets from cosmological observations allow us to determine the values of these parameters and their implications Discrepancies (or inconsistencies) between the parameter values as determined from different data sets can signal systematic errors in the data or problems with the underlying cosmological model Mustapha Ishak, AAS Denver

4 A new measure of discordance: Index of Inconsistency (IOI) Lin & Ishak, PRD 96, (2017) arxiv: IOI can find inconsistencies when present between two or multiple data sets IOI can quantify the degree of inconsistency using a numerical scale : IIIIII 1 no significant inconsistency IIIIII 5 very strong inconsistency The essence of the IOI statistical measure is that it sums up the statistical difficulty of each data sets to support the joint analysis Mustapha Ishak, AAS Denver

5 Application to current data sets: Geometry data versus structure growth data: IOI=4.3 for LCDM and 5.4 for wcdm Mustapha Ishak, AAS Denver

6 Tensions between Hubble parameter, HH 0, values Lin & Ishak, Phys. Rev. D 96, (2017) arxiv: Values of HH 0 from different data sets IOI values between different data sets We find a strong inconsistency or tension between the local measurement of HH 0 and the one from Planck space mission Mustapha Ishak, AAS Denver

7 Planck CMB versus Large Scale Structure data sets A persistent tension up to the high-end of the moderate range (close to the strong range) Mustapha Ishak, AAS Denver

8 Concluding remarks We developed mathematical measures to quantify the degree of inconsistency between data sets. We found a strong discordance between the values of the Hubble parameter from local measurement and Planck measurement. We found inconsistencies between large scale structure data and Planck data. These can be caused by systematic errors in the data sets or problems with the standard model of cosmology. The Hubble parameter discrepancy can be the smoking gun of issues with the standard model of cosmology. Mustapha Ishak, AAS Denver

9 Additional slides below are not used during talk. Mustapha Ishak, TSAPS 2017 Dallas 9

10 Our work from sometime ago: Consistency between growth rate of structure and expansion as a test of cosmic acceleration (MI, Upadhye, and Spergel, PRD 2006, astro-ph 2005) For a dark energy wcdm model, the expansion history is given by: and the Growth rate G(a=1/(1+z)) is given by integrating: For Modified Gravity DGP models and k=0, the expansion history is given by and the growth rate of function is given by H δ 4πGρ 1 + δ = 3β δ G '' H ( z) = Ho (1 Ω ' 3 w( a) G 2 1+ X ( a) a de + )(1 + ε ( z) G ( a) = D( a) ; a Equation (1) and (2) must be mathematically consistent one with another via General Relativity. Equation (3) and (4) must be consistent one with another via DGP theory z) 3 + Ω 3 1 w( a) 2 1+ X ( a) G 2 a de = 0; H ( z) = Ho (1 Ωm) + (1 Ωm) + Ωm(1 + z) (1) (3) δ ( a) D ( a) = δ (1) H β = 1 2r c H H Mustapha Ishak, TSAPS 2017 Dallas 10 (2) (4)

11 IOI for growth versus geometry for the ΛCDM model Mustapha Ishak, TSAPS 2017 Dallas 11

12 IOIs for the wcdm model: geometry vs growth Mustapha Ishak, TSAPS 2017 Dallas 12

13 Relative drop in IOI and relative residual in IOI for individual parameters in the wcdm model Mustapha Ishak, TSAPS 2017 Dallas 13

14 Definitions and quantities used in the work Mustapha Ishak, TSAPS 2017 Dallas 14

15 Data in second IOI paper Lin & MI, 2017 Mustapha Ishak, TSAPS 2017 Dallas 15

16 Comparison to other measures of consistency/inconsistency in the literature Comparison between IOI and these quantities provided in the paper Mustapha Ishak, TG-2017 Vancouver 16

17 Mustapha Ishak, TSAPS 2017 Dallas 17

18 IOI Captures various cases of inconsistencies. Here are two toy experiments for each type of inconsistency. Mustapha Ishak, TSAPS 2017 Dallas 18

19 Zooming in an individual cosmological parameter IIIIII ii : Relative drop in the index of inconsistency after marginalization over a given parameter pp ii IIIIII ii : Relative residual index of inconsistency for a given parameter pp ii after marginalization over all the other parameters For consistency between two or more experiments for a given parameter, both of the corresponding relative drop and relative residual IOIs must be small. Mustapha Ishak, TSAPS 2017 Dallas 19

20 Using the growth rate of large-scale structure (cluster and superclusters of galaxies) At least two methods to test gravity using cosmology have been used: 1) Looking for inconsistencies between cosmological parameter spaces as determined by the growth data versus the geometry/expansion data (e.g. MI, Upadhye, and Spergel, PRD 2006; Wang et al., 2007; Ruiz & Huterer, 2015; Bernal, Verdi, Cuesta, 2016, ) 2) Defining parameters for the growth rate and constraining them using data sets (e.g. Linder, 2005; Koyama, 2006; Bertschinger and Zukin, 2008; and many others in this meeting ) We used both methods over the years but I will focus on (1) here Mustapha Ishak, AAS Denver

21 Examples: MI, Upadhye, and Spergel, Phys.Rev. D74 (2006) ). Is Cosmic Acceleration a Symptom of the Breakdown of General Relativity? We simulated the data using modified gravity (DGP) but then we fit the data to dark energy models => a detectable inconsistency in the simulated data Ruiz, Huterer, Phys. Rev. D 91, (2015) Banana Split: Testing the Dark Energy Consistency with Geometry and Growth Bernal, Verde, Cuesta, JCAP02(2016)059, Parameter splitting in dark energy: is dark energy the same in the background and in the cosmic structures? Mustapha Ishak, AAS Denver

22 Our new work: How to quantify the degree of inconsistency? Lin & MI, PRD 96, (2017) arxiv: We introduced a new measure Need to introduce a mathematical measure that takes into account 3 aspects of inconsistencies: a) deviation between likelihood maxima b) volume of covariance matrices (ellipsoid sizes) c) degeneracy directions (ellipsoid orientations) d) Other practical properties (e.g. invariance) 22

23 Index of Inconsistency (IOI) Lin & MI, PRD 96, (2017) arxiv: We consider two experiments and define where Mustapha Ishak, AAS Denver

24 Index of Inconsistency (IOI) Lin & MI, PRD 96, (2017) arxiv: In the Gaussian limit We define the IOI as: Generalized to multiple experiments: Where and Other works defined other quantities (e.g. Marshall, Rajguru, Slosar, 2006; March, Trotta, Amendola, Huterer, 2011; Verdi, Protopapas, Jimenez, 2013; Seehars, Grandis, Amara, Refregier, 2016; Grandis, Rapetti, Saro, Mohr, 2016) Mustapha Ishak, AAS Denver

25 Flowchart of algorithmic procedure developed and applied using IOI measures to identify cause of inconsistency Lin & MI, Phys. Rev. D D 96, (2017) arxiv: Jeffreys scales, Theory of Probability, Oxford Classic Texts in the Physical Sciences (Oxford, 1998). Mustapha Ishak, TSAPS 2017 Dallas 25

26 Planck CMB (temperature, polarization) and Large Scale Structure data sets (clustering, lensing, RSD, SZ) Moderate tension between Planck temperature and polarization Large Scale Structure data sets consistent with each other thus fine to combine Mustapha Ishak, AAS Denver