Search for Cosmic Strings in the COSMOS Survey

1. 1st IAS School on Particle Physics and Cosmology and Implications for Technology 9-31 January 2012 Nanyang Technological University, Singapore Search for Cosmic Strings in the COSMOS Survey Ivan P. W. Teng Department of Physics, National University of Singapore

2. Outline • Cosmic strings: What they are and their formation • Why look for cosmic strings? • Is cosmic string theory = string theory? • Recent attempts on cosmic string detection • Searching for cosmic strings in the COSMOS survey based on their gravitational lensing signature – detection methodology, observations (analysis, detection efficiency), establishing limits on cosmic string energy-density and mass density • Conclusion

3. What are cosmic strings? • Hypothetical one-dimensional topological defects thought to have been formed in the early universe during the first fraction of a second after the Big Bang • A result of phase transitions occurring in different regions of spacetime as the early universe cooled Radiation-dominated era (1000 years after Big Bang) Matter-dominated era (10000 years after Big Bang) (Cambridge Cosmology Group)

4. Formation of Cosmic Strings First-order phase transitions: (Cambridge Cosmology Group) • Bubble nucleation of early matter in the universe • Expanding bubbles of a new phase (true vacuum) meet each other, with a phase transition complete when these bubbles expand until the old phase (false vacuum) disappears • Nucleation of matter gives rise to cosmic strings Second-order phase transitions: • Second-order phase transitions proceed smoothly - the old phase transforms itself into the new phase in a continuous manner

5. Why do we look for cosmic strings? • Various cosmological models (string cosmology) hypothesize their existence • May explain about the formation of large-scale structure, observed but still not sufficiently understood • Earliest relics; greater knowledge about the early universe in the immediate moments after the Big Bang

6. Cosmic String Theory ≠ String Theory • ‘string’ should be taken as descriptor for the geometric shape of a cosmic string • Common hypothetical link between cosmic strings and string theory: production of cosmic strings during the last stages of brane inflation [1], [2] • “String theory cosmologists have discovered cosmic strings lurking everywhere in the undergrowth…” ------ T. W. B. Kibble [3] [1] Brane Inflation Gia Dvali, S.-H. Henry TyePhys.Lett. B450 (1999) 72-82 [2] Cosmic string production towards the end of braneinflation SaswatSarangi, S.H.HenryTyePhys.Lett. B536 (2002) 185-192 [3] Cosmic Strings Reborn? T.W.B. Kibble http://arxiv.org/pdf/astro-ph/0410073.pdf

7. Composition of the Universe (NASA WMAP Science Team)

8. First systematic search for cosmic strings based on light from distant galaxies: http://physicsworld.com/cws/article/news/34826 “…… “ ***Cosmic strings <2%

9. Recent attempts on detection of cosmic strings • Precise observations of the cosmic microwave background(CMB) and galaxy surveys predict the evolution of the universe out of random gaussianfluctuations, hence ruling out the contribution of cosmic strings towards large-scale clumping of matter in the universe • Present detections of cosmic strings involve analyzing CMB anisotropies and gravitational lensing observations - gravitational lensing of a galaxy by a straight section of string produces two identical and undistorted images of the galaxy • Prominent example of a failure – CSL-1 in January 2006 • Peculiar double extragalactic object CSL-1 observed by HST and thought to be the result of gravitational lensing by a cosmic string

10. (M. Sazhin et. al., Mon. Not. R. Astron. Soc. 000, 1–6 (2005)) http://arxiv.org/pdf/astro-ph/0601494.pdf • Further observations showed that it is actually an image of a pair of elliptical galaxies, in spite of their similar energy and light distributions and both show clear signs of interaction

11. Recent attempts on the search of cosmic strings • E. Morganson, P. Marshall, T. Treu, T Schrabback andR. D. Blandford • "Direct Observation of Cosmic Strings via their Strong Gravitational Lensing Effect: II. Results from the HST/ACS Image Archive“;Mon.Not.Roy.Astron.Soc, Vol. 406, Issue 4, pg. 2452–2472, August 2010 • E. Jeong, C. Baccigalupi and G. F. Smoot • "Probing Cosmic Strings with Satellite CMB Measurements"; Journal of Cosmology and Astroparticle Physics, Issue 09, pp. 018, 2010 • J.L. Christiansen, E. Albin, T. Fletcher, J. Goldman, I.P.W. Teng, M. Foley and G.F. Smoot • "Search for Cosmic Strings in the COSMOS Survey"; Phys. Rev. D83: 122004, 2011

12. Search for cosmic strings based on their gravitational lensing signature Gravitational Lensing: (NASA) • Gravity from a massive object warps spacetime and bends everything in its gravitational field, including light rays from a bright background source • Observer sees multiple images of the same source

13. Search for cosmic strings based on their gravitational lensing signature • Any plausible observational evidence for the existence of cosmic strings is based heavily on the interactions of cosmic strings with gravity Conical space-time around a cosmic string: (Berkeley Center for Cosmological Physics)

14. Search for cosmic strings based on their gravitational lensing signature • Conical deficit angle: angle which results in the observed lensing effect of a pair of image galaxies on both sides of the string • Projecting conical space-time of a string onto flat space-time:

15. Search for cosmic strings based on their gravitational lensing signature What we are looking for:

16. Search for cosmic strings based on their gravitational lensing signature • = deficit angle •  = opening angle • G/c2 = cosmic string mass per unit length • = string tilt angle • Dls = distance between cosmic string l and lensed background object s • Dos = distance between observer o and lensed background object s

17. Detection Methodology (COSMOS Survey (HST ACS))

18. Detection Methodology • Cosmic Evolution Survey • Two square degree equatorial field of the sky (in the constellation of the Sextans) • 9 X 9 mosaic comprising 81 scientific images observed on the I-band of the HST’s Advanced Camera for Surveys (ACS) • SExtractor, IDL • Images that make up survey edges are excluded

19. Detection Methodology Selection of resolved galaxies: • SExtractor and IDL to select resolved objects from the FITS images from the COSMOS public archives after comparison with the “official” COSMOS catalog[4] • “Resolved objects” – galaxies that are potentially lensed by cosmic strings • Removal of stars and spurious detections (objects that are too small to be consistent with the point spread function) from SExtractor-generated catalogs, as well as objects that are not present in the “official” COSMOS catalog [4] Caltech, "COSMOS Public Archives"; http://irsa.ipac.caltech.edu/data/COSMOS

20. Detection Methodology • Black points – resolved galaxies • Dark grey points – point sources including stars • Light gray points – spurious detections too small to be consistent with the point spread function

21. Detection Methodology • Data pertaining redshift of objects in the COSMOS survey is incomplete and unreliable • Need to assign redshifts to these objects • Redshifts are randomly assigned to the resolved galaxies according to their MAG_AUTO values based on [5], which are equivalent to their I-band magnitudes Nsrc(zs) = number of galaxies present zm = assigned redshiftbased on the galaxy's I-band magnitude I [5] R. Massey, J. Rhodes, A. Refregier et al, "Weak Lensing from Space II: Dark Matter Mapping"; Astrophysical Journal 127: 3089-3101, 2004

22. Detection Methodology

23. Detection Methodology Simulation of cosmic strings: • Statistically determine the possible number of resolved galaxies that would have been lensed in the presence of a cosmic string through monte-carlo simulations, if the opening angle placing the image-galaxy on the side of the simulated string opposite the true-galaxy is equal to or smaller than 15’’ – for simulation of cosmic string signals • >>> Catalog-level simulation • Laying sample cosmic strings of a specific redshift and energy-density/relative tilt ---------- pixel-by-pixel embedding of galaxy pairs into the original FITS images (postage stamping of lensed galaxy on opposite side of cosmic string, with Lee filtering to reduce noise) – to understand efficiencies of detection methodology • >>> Image-level simulation (Galaxy pairs, merged galaxies, sliced galaxies)

24. Detection Methodology Selection of matched galaxy pairs: • Every resolved galaxy paired up with every other galaxy in the SExtractor catalog, with the only condition that the opening angle  of each pair is smaller than 15’’ • The two galaxies in the pair are analyzed for their morphological similarity based on their brightness and shape • Done by determining their correlation and cross-correlation on the pixel level – pixel-by-pixel comparison between the two galaxies in the pair in terms of pixel intensity • Further cuts based on magnitude, shape and orientation based on ELLIPTICITY, FWHM_IMAGE, MU_MAX and THETA_IMAGE variables of the galaxies in the pair to further improve on the cosmic string signal-to-noise ratio • >>> Based on the ratio of the difference in magnitude(size) of the two variables in the galaxy pair to the error for the variables in the pair/magnitude of each variable in the pair

25. Detection Methodology Identical galaxies have a perfect correlation of 0, while galaxies that are totally different from each other have a correlation of ±1.

26. Detection Methodology A cross-correlation of 1 suggests that both galaxies are identical, while galaxies that are totally different from each other have a cross-correlation of 0.

27. Detection Methodology

28. Detection Methodology Selection of matched galaxy pairs: • Every resolved galaxy paired up with every other galaxy in the SExtractor catalog, with the only condition that the opening angle  of each pair is smaller than 15’’ • The two galaxies in the pair are analyzed for their morphological similarity based on their brightness and shape • Done by determining their correlation and cross-correlation on the pixel level – pixel-by-pixel comparison between the two galaxies in the pair in terms of pixel intensity • Further cuts according to magnitude, shape and orientation (ELLIPTICITY, FWHM_IMAGE, MU_MAX and THETA_IMAGE variables) of the galaxies in the pair to further improve on the cosmic string signal-to-noise ratio • >>> Based on the ratio of the difference in magnitude(size) of the two variables in the galaxy pair to the error for the variables in the pair/magnitude of each variable in the pair

29. Detection Methodology

30. Detection Methodology

31. Efficiency

32. Bold line: zl = 0.25 • Dotted line: zl = 0.50 • Dashed line: zl = 0.75 • Dash-dot line: zl= 1.00 • Dash-dot-dot-dot line: zl = 1.25 • Long dashes zl= 1.50

33. Bold line: zl = 0.25 • Dotted line: zl = 0.50 • Dashed line: zl = 0.75 • Dash-dot line: zl= 1.00 • Dash-dot-dot-dot line: zl = 1.25 • Long dashes zl= 1.50

34. Bold line: zl = 0.25 • Dotted line: zl = 0.50 • Dashed line: zl = 0.75 • Dash-dot line: zl= 1.00 • Dash-dot-dot-dot line: zl = 1.25 • Long dashes zl= 1.50

35. Bold line: zl = 0.25 • Dotted line: zl = 0.50 • Dashed line: zl = 0.75 • Low zl below 1.00: detection efficiency generally independent of zl and consistent with increasing string energy density sin, regardless of tilt angle  • Absence of matched galaxy pairs with opening angles at 0.40” and smaller, as a result of the merging of galaxies by SExtractor • Depending on , galaxy merging is evident for light cosmic strings with sin smaller than approximately 0.30” and zl greater than 0.50, where the loss of matched pairs and hence cosmic string signal translates to zero efficiency in this region

36. Dash-dot line: zl= 1.00 • Dash-dot-dot-dot line: zl = 1.25 • Long dashes zl= 1.50 • High zl above 1.00: improved detection efficiency with increasing zl and sin - detection methodology generally workswell for detecting massive cosmic strings at high zl • Light cosmic strings at low sin and zl above 1.00: relatively poor efficiencies as evident in the zero efficiencies at sin below 2.00” - attributed to dim galaxies at high redshifts being embedded, whereby at small opening angles and hence low sin, matched pairs from these galaxies are likely lost as noise during Lee filtering >>> zero efficiency • Observed spikes in efficiencies from zero likely due to well defined resolved galaxies embedded but whose original magnitude may have been dimmed as a result of Lee filtering, and whose final magnitudes then correspond to high redshifts

37. Bold line: zl = 0.25 • Dotted line: zl = 0.50 • Dashed line: zl = 0.75 • Dash-dot line: zl= 1.00 • Dash-dot-dot-dot line: zl = 1.25 • Long dashes zl= 1.50 • Overall inconsistent behaviour of detection efficiencies as evident in high zllikely due to higher-than-desired noise levels introduced during the embedding process at higher redshifts

38. Bold line:  = 0 • Dotted line:  = 15 • Dashed line:  = 30 • Dash-dot line: = 45 • Dash-dot-dot-dot line:  = 60 • Long dashes: = 75 • Dotted line:  = 90

39. Bold line:  = 0 • Dotted line:  = 15 • Dashed line:  = 30 • Dash-dot line:  = 45 • Dash-dot-dot-dot line:  = 60 • Long dashes:  = 75 • Dotted line:  = 90

40. Detection efficiencies tend to be dependent on  with increasing zl, especially for the detection of light cosmic strings with low sin • At low zlbelow 1.00, efficiencies are relatively consistent regardless of  • At high zlabove 1.00, however, efficiencies of detecting strings with low sin become increasingly dependent on  • Observed trend: efficiencies tend to be poor at low sin for = 0and 90, which is especially the case at zl= 1.25 and 1.50

41. Matched Pairs Distribution • Matched galaxy pairs obtained from respective cuts are binned according to their opening angles and their distributions plotted on a normalized background distribution of galaxy • pairs • Background galaxy pairs – galaxy pairs matched from resolved galaxies in the SExtractor catalog with no cuts applied to them • Background distribution prepared by statistically normalizing its galaxy pairs, with opening angles ranging between 7” and 15”, to the number of morphologically similar lensed galaxy pairs (i.e. matched galaxy pairs) with opening angles over the same range • Range chosen as massive cosmic strings producing lensed galaxy pairs with opening angles greater than 7” have been ruled out to exist[6] [6] L. Pogosian, S.-H.H. Tye, I. Wasserman and M. Wyman, "Observational constraints on cosmic string production during brane inflation"; Phys. Rev. D68: 023506, 2003

42. Matched Pairs Distribution • Detection methodology does not solely encompass the search for perfectly straight cosmic strings • Use of a range of string tilt angles highlights ability of methodology to cater to very long cosmic strings that are moderately curved, and therefore likely tilted at various • angles when they appear to be straight in the fiducial regions being analyzed, as a result of the strings being very long • Note that the above statement is valid only when no kink is present at any point along the length of the cosmic string; same assumption made with regards to the formulation of the detection methodology

43. Matched Pairs Distribution sin = 4.00”, zl = 0.50,  = 75

44. Between approximately 0” and 0.40”, no galaxy pairs are present in the background distribution • Absence of galaxy pairs within this range of opening angles is attributed to merging of galaxies with opening angles smaller than 0.40” by SExtractor, while at 0.40” and above the background galaxy pairs and the matched pairs increase linearly as expected with increasing opening angle • Two curves in each of the figures representing the same set of simulated data at the catalog-level • Lower curve includes inefficiencies in the detection methodology that has been accounted for; upper curve consists of simulated matched pairs with no detection inefficiency taken into account

45. Matched Pairs Distribution • p-values range between approximately 7% to 27% • No observed evidence for an excess of matched pairs between 0.40” and 7.00” that suggests the existence of cosmic strings in the COSMOS survey, based on matched pairs distribution plots and p-values

46. Establishing limits • Observational data from the COSMOS survey may be used to establish limits on the types of cosmic strings that may exist according to their characterizing parameters (sin, zl, and ), based on the detected strength of the cosmic string signals represented by the number of matched galaxy pairs observed • Adopt classical one-sided Neyman statistics for such a purpose • Add up galaxy pairs with opening angles between 0.40” and 7.00” from simulated cosmic string signals, as well as the observed matched galaxy pairs based on the optimized correlation and variable cuts and also the random galaxy pairs making up the background over a similar opening angle range for cosmic string signal pairs • Apply one-sided classical Neyman 95% confidence limits: nlimit = the minimum number of galaxy pairs that are consistent with statistical fluctuations in the background

47. Establishing limits nx = number of galaxy pairs observed either due to the existence of cosmic strings or background statistical fluctuations  = nobserved matched pairs - nbackground pairs = the overall number of galaxy pairs whose images are morphologically similar • Any excess number of galaxy pairs giving rise to nx > nlimit may be said with 95% confidence that these galaxy pairs must be due to cosmic strings and not from background fluctuations • Implies that any combination of cosmic string parameters producing galaxy pairs nsimulated signal pairs, based on the simulated cosmic string data, greater than nlimit may be excluded on a 95% confidence level as no cosmic strings are observed in the COSMOS survey • If cosmic strings exist it must be nsimulated signal pairs < nlimit(where nx = nsimulated signal pairs in this case), i.e. to the left side of the Gaussian distribution where cosmic string signals cannot be distinguished from the background fluctuations

48. Assigning confidence limits: nsimulated signal pairs < nlimit nsimulated signal pairs > nlimit

49. Establishing limits  = 45  = 90 • Out to a string redshiftzl of between 0.70 and 0.80, no evidence of cosmic strings has been found • 95% upper confidence limit may be placed on G/c2 < 0.3  10-6 • Corresponds to the mass of lightest cosmic strings that may be found, should cosmic strings exist

50. Establishing limits nsimulated signal pairs > nlimit nsimulated signal pairs < nlimit • “Excluded”= cosmic strings with such characterizing parameters may be • excluded with 95% confidence = nsimulated signal pairs > nlimit • i.e. no cosmic strings are observed in the COSMOS survey for cosmic strings with such characterizing parameters • ‘Not Excluded” = nsimulated signal pairs < nlimit • i.e. if cosmic strings exist, they must have such characterizing parameters whereby their signals cannot be distinguished from the background fluctuations (to the left side of the Gaussian distribution)