
854 A.2d 97 (2004)
84 Conn.App. 561
Robert TORRES
v.
COMMISSIONER OF CORRECTION.
No. 23794.
Appellate Court of Connecticut.
Submitted on briefs April 26, 2004.
Decided August 17, 2004.
Jonathan K. Gable, special public defender, filed a brief for the appellant (petitioner).
James E. Thomas, state's attorney, and Toni M. Smith-Rosario and Angela R. Macchiarulo, assistant state's attorneys, filed a brief for the appellee (respondent).
LAVERY, C.J., and FOTI and DIPENTIMA, Js.
LAVERY, C.J.
The petitioner, Robert Torres, appeals from the habeas court's dismissal of his petition for a writ of habeas corpus. On *98 appeal, the petitioner claims that the court improperly (1) concluded that he was provided with effective assistance of counsel and (2) required him to present expert testimony to demonstrate that his trial counsel's performance was deficient. We affirm the judgment of the habeas court.
In December, 1995, a jury convicted the petitioner of conspiracy to commit murder in violation of General Statutes §§ 53a-48 and 53a-54a, attempt to commit assault in the first degree in violation of General Statutes §§ 53a-49(a)(2) and 53a-59(a)(1), and risk of injury to a child in violation of General Statutes § 53-21.[1] The petitioner appealed from the conviction to this court, which reversed the conviction of attempt to commit assault in the first degree and upheld the conviction of the remaining two counts. State v. Torres, 47 Conn.App. 205, 703 A.2d 1164 (1997).
Following his appeal, the petitioner filed an amended petition for a writ of habeas corpus on August 15, 2001. Therein, he alleged that his state and federal constitutional rights were violated because his trial attorney, John Stawicki, failed to provide effective assistance in that but for counsel's unprofessional errors and omissions and failures to investigate, the petitioner would not have been found guilty of the charges. After a hearing, the court concluded that the petitioner had failed to produce sufficient evidence to overcome the strong presumption that counsel's conduct fell within the wide range of reasonable professional assistance. The court thereafter granted the petition for certification to appeal to this court.

I
The petitioner first claims that the court improperly concluded that he was provided with effective assistance of counsel. Specifically, the petitioner argues that his counsel failed to pursue pretrial motions relative to the suppression of evidence and statements allegedly attributed to the petitioner, and failed to investigate the case properly and to advise the petitioner of his findings.[2] We disagree.
As an initial matter, we set forth our standard of review. "Our standard of review in a habeas corpus proceeding challenging the effective assistance of trial counsel is well settled. Although a habeas court's findings of fact are reviewed under the clearly erroneous standard of review ... [w]hether the representation a defendant received at trial was constitutionally inadequate is a mixed question of law and fact.... As such, that question requires plenary review by this court unfettered by the clearly erroneous standard....
"The petitioner's right to the effective assistance of counsel is assured by the sixth and fourteenth amendments to the federal constitution, and by article first, § 8, of the constitution of Connecticut. In Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), the United States Supreme Court established that for a petitioner to prevail on a claim of ineffective assistance of counsel, he must show that counsel's assistance was so defective as to require reversal of [the] conviction.... That requires the petitioner *99 to show (1) that counsel's performance was deficient and (2) that the deficient performance prejudiced the defense.... Unless a [petitioner] makes both showings, it cannot be said that the conviction ... resulted from a breakdown in the adversary process that renders the result unreliable." (Citation omitted; internal quotation marks omitted.) Toccaline v. Commissioner of Correction, 80 Conn.App. 792, 797-98, 837 A.2d 849, cert. denied, 268 Conn. 907, 845 A.2d 413 (2004). We now address each of the petitioner's arguments in turn.

A
The petitioner first argues that Stawicki's failure to pursue pretrial motions to suppress evidence deprived him of his constitutional right to the effective assistance of counsel. Specifically, the petitioner contends that the two statements he gave to the police after receiving Miranda[3] warnings and signing waiver forms were involuntary and, therefore, should have been the subject of a motion to suppress.[4] We are not persuaded.
When reviewing the habeas court's findings concerning the voluntary nature of the petitioner's statements, our review is plenary. "On the ultimate issue of voluntariness ... we will conduct an independent and scrupulous examination of the entire record to ascertain whether the trial court's finding is supported by substantial evidence." (Internal quotation marks omitted.) State v. Byrd, 239 Conn. 405, 408, 685 A.2d 669 (1996). We must remember, however, that "[t]he habeas judge, as the trier of facts, is the sole arbiter of the credibility of witnesses and the weight to be given to their testimony." Velez v. Commissioner of Correction, 57 Conn.App. 307, 309, 748 A.2d 350 (2000).
After a thorough review of the entire record, we conclude that there was substantial evidence to support the court's finding that the petitioner's statements were given voluntarily. The court heard the testimony of the petitioner, Stawicki and James Rovella, a detective with the Hartford police department to whom the petitioner gave his statement. The court also had before it the transcript of the initial trial and the two waiver of rights forms connected with the statements in question. On the basis of that record, the court found that "[a]fter Detective Rovella had properly advised the petitioner of his rights to silence and representation, the petitioner waived his rights and provided a voluntary oral statement to the police." (Emphasis added.) Deferring to the court's assessments of credibility, we must accept the fact that the court credited the testimony of Stawicki and Rovella over the petitioner's statements. Having reviewed the record and briefs, we determine that there was substantial evidence to support the court's finding that the petitioner's statements were given voluntarily. Accordingly, we conclude that Stawicki's representation was not deficient for his failure to pursue suppression of the petitioner's statements.


*100 B
The petitioner further argues that Stawicki was ineffective in that he failed to investigate the case adequately and to advise him of his findings. We are not persuaded.
"While it is incumbent on a trial counsel to conduct a prompt investigation of the case and explore all avenues leading to facts relevant to the merits of the case and the penalty in the event of conviction ... counsel need not track down each and every lead or personally investigate every evidentiary possibility.... In a habeas corpus proceeding, the petitioner's burden of proving that a fundamental unfairness had been done is not met by speculation, but by demonstrable realities.... One cannot successfully attack, with the advantage of hindsight, a trial counsel's trial choices and strategies that otherwise constitutionally comport with the standards of competence." (Citations omitted; internal quotation marks omitted.) Ostolaza v. Warden, 26 Conn.App. 758, 765, 603 A.2d 768, cert. denied, 222 Conn. 906, 608 A.2d 692 (1992).
The court found that Stawicki had conducted an investigation of the case that included interviewing Rovella and the Federal Bureau of Investigation agent who was present at the giving of the petitioner's second statement, and an attempt to interview the state's eyewitnesses. Furthermore, Stawicki presented an alleged eyewitness, Petra Vargas, who testified in the petitioner's favor. The petitioner did not identify any other witnesses whom Stawicki might have called to testify at trial, nor did he present the substance of the testimony of these witnesses as evidence at his habeas proceeding. To find that the failure to interview those alleged witnesses amounted to ineffective assistance of counsel that prejudiced the petitioner would be mere speculation. Because this court will not engage in speculation, but is constrained to evaluating "`demonstrable realities'"; id.; we conclude that counsel's representation was not deficient.

II
The petitioner's final claim is that the court improperly required the presentation of expert testimony to determine if Stawicki's performance was deficient. We disagree.
"Whether expert testimony is required in a particular case is determined on a case-by-case basis and its necessity is dependent on whether the issues are of sufficient complexity to warrant the use of the testimony as assistance to the habeas court.... It is the habeas court, therefore, that must initially decide whether, in order to make intelligent findings, it needs expert testimony on the question that it must decide.... A trial court has broad discretion in determining whether expert testimony is needed." (Citations omitted.) Johnson v. Commissioner of Correction, 34 Conn.App. 153, 158, 640 A.2d 1007, cert. denied, 229 Conn. 919, 644 A.2d 914 (1994).
Although the petitioner characterizes the court's ruling as requiring expert testimony, our review of the decision reveals that the court found that no credible evidence, expert or otherwise, had been presented in support of the petitioner's claims. The court stated that "[t]he failure of the petitioner to bring any expert testimony before this court leaves the court without any evidence to determine if the performance of the trial counsel was deficient." The court further found, however, that the petitioner did not present any evidence at all in support of his claim that Stawicki's performance was deficient.
Specifically, the court stated that "[w]hat was lacking from the petitioner's *101 case is any evidence by which this court could conclude that the failure [to act] was substandard performance by the trial counsel." (Emphasis added.) When discussing counsel's failure to pursue the motions for suppression, the court found that "[t]here has been no proof, either in the form of questions directly put to the trial counsel, or in the form of expert opinion that would permit this court to find any basis for filing such motions." (Emphasis added.) The court concluded by stating that "[i]n the absence of any evidence that tends to establish that there was a good faith basis to file such suppression motions, the court will not question the trial tactics of a trial defense counsel who declines to do so."
On the basis of our review of the record, we conclude that the court properly determined that no evidence was presented from which it could find that Stawicki's performance was deficient.[5]
The judgment is affirmed.
In this opinion the other judges concurred.
NOTES
[1]  We note that the jury acquitted the petitioner on charges of murder in violation of General Statutes § 53a-54a and assault in the second degree with a firearm in violation of General Statutes §§ 53a-60a and 53a-60(a).
[2]  At his habeas trial, the petitioner also claimed that Stawicki failed to object to improper jury instructions regarding the risk of injury charge. The petitioner failed to brief the issue on appeal and, therefore, we deem that claim abandoned. See, e.g., Mitchell v. Commissioner of Correction, 68 Conn.App. 1, 8, 790 A.2d 463, cert. denied, 260 Conn. 903, 793 A.2d 1089 (2002).
[3]  See Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966).
[4]  In his brief, the petitioner also contends that Stawicki failed to file a motion to suppress certain evidence used against him that was taken from his house pursuant to a search warrant in violation of his fourth amendment rights. The petitioner, however, has failed to set forth either the factual background or the appropriate legal framework in which to analyze that aspect of his claim. Because that aspect of his claim is not adequately briefed, we decline to afford it review. See State v. Parrott, 262 Conn. 276, 290 n. 18, 811 A.2d 705 (2003).
[5]  In light of that conclusion, we need not address the petitioner's argument that the court improperly required expert testimony to determine whether trial counsel's performance was deficient.
